Slice profile

The integral describes the spatial amplitude modulation of the excited magnetization. It represents the excitation or slice profile, g(z), of the pulse in real space. As drops to zero for t outside the pulse, the integration limits can be extended to infinity whereupon it is seen that the excitation profile is the Fourier transfonn of the pulse shape envelope ... 

Fig. 12. Sequences for volume selective single voxel spectroscopy. Both techniques work with three slice-selective RF-pulses. (a) The Point RESolved Spectroscopy (PRESS) sequence generates a volume selective double spin-echo. The entire time delay between the initial 90° excitation and the echo is sensitive to transverse relaxation, (b) The Stimulated Echo Acquisition Mode (STEAM) sequence generates a stimulated echo. Maximal signal intensity (without relaxation effects) is only half the signal intensity of PRESS under comparable conditions, but slice profiles are often better (only 90° pulses instead of 180° pulses) and the TM interval is not susceptible to transverse relaxation, (c) The recorded echo signal is only generated in a volume corresponding to the intersection of all three slices.

Fig. 1.8. Effective slice width in spiral/helical CT the collimated slice profile, which is a trapezoidal in general, is indicated in red. The slice sensitivity profiles (SSP) after spiral/ helical interpolation are bell-shaped see the green curves for the most commonly used single-slice approach (180-LI) at dif-...

Clinical MR scanners used for fast imaging experiments may have up to 15 kW RF amplifiers. These high powers are necessary to reduce pulse duration in fast spin-echo imaging sequences. However, care must be taken that the amplifiers are linear otherwise the shaped pulses necessary for slice selection will be distorted and the slice profile degraded. Of course, many manufacturers are aware of this problem and compensate their pulse shapes for the known distortions induced by the RF amplifier so that the final pulse shape delivered to the RF coil is optimal. If slice profiles are inadequate it is always worth checking for non-linearity in the RF amplifiers. 

Baseline Compensation Analysis—To compensate for baseline drift and signal offset, subtract an area slice profile of a blank run from the sample run to obtain corrected area slices. This profile is obtained as follows ... 

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

The graphs of each of the species concentrations are plotted as a function of position along the tube z and time t. At the edges of the graphs for the concentrations of A and B we see the boundary and initial conditions. All values are unit or zero concentration as we had specified. As we move through time, we see the concentrations of both species drop monotonically at any position. Furthermore, if we take anytime slice, we see that the concentrations of reactants drop exponentially with position—as we know they should. At the longer times the profiles of... 

The density profile for the micropore fluid was determined as In the equilibrium simulations. In a similar way the flow velocity profile for both systems was determined by dividing the liquid slab Into ten slices and calculating the average velocity of the particles In each slice. The velocity profile for the bulk system must be linear as macroscopic fluid mechanics predict. 

R. Kuchenbuch and A. Jungk, A method for determining concentration profiles at the soil-root interface by thin slicing rhizospheric soil. Plant Soil 68 391 (1982). R. Schonwitz and H. Ziegler, Quantitative and qualitative aspects of a developing rhizosphere microflora of hydroponically grown maize seedlings. Z Pflanzenernahr. Bodenk. 749 623 (1986). 

R. Kuchenbuch and A. Jungk, A inethod for determining concentration profiles at the soil-root interface by thin slicing rhizospheric soil. Plant Soil 68 39 (1982). 

The shape of any rf pulse can be chosen in such a way that the excitation profile is a rectangular slice. In the light of experimental restrictions, which often require pulses as short as possible, the slice shape will never be perfect. For instance, the commonly used 900 pulse is still acceptable, while a 1800 pulse produces a good profile only if it is used as a refocusing pulse. Sometimes pulses of even smaller flip angles are used which provide a better slice selection (for a discussion of imaging with small flip angles, see Section 1.7). 

The profiling method requires the sensitive slice to be shifted through the object. Figure 2.4.2 shows the mechanical lift used to move the sensor with respect to the sample. The object under study, for instance the lower surface of the arm in the picture, is positioned on top of a flat holder (A) and the NMR sensor is placed under it on a movable plate (B). The mechanical construction allows one to move the sensor up and down with a precision of 10 pm. The distance between the rf coil and the sensitive slice defines the maximum penetration depth into the sample (maximum field of view of the ID image). Depending on the application, the position of the rf coil with respect to the sensitive slice can be changed to maximize the sensitivity. 

The slice selection procedure can be combined with a number of pulse sequences to spatially resolve NMR parameters or to contrast the profiles with a variety of filters. The most commonly used acquisition schemes implemented to sample echo train decays are the CPMG [(jt/2)0—(Jt)90] or a multi-solid echo sequence [(jt/ 2)0-(jt/2)9o]. In these instances, the complete echo train can be fitted to determine... 

Fig. 2.8.6 (a) (i) I implementation of vertical cylindrical Couette cell using concentric glass tubes (ii) velocity image taken across a horizontal slice and (iii) velocity profile taken across the cell. Note that the marker fluid in the inner cylinder exhibits rigid body motion... 

Fig. 2.8.7 (a) Implementation of cone-and-plate device, (b) Velocity image taken across a vertical slice, (c) Velocity profile taken across the cell with 7° cone angle. Note the highly linear variation of velocity (adapted from Ref. [15]). 

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