Slicing Volume

Techniques of tumor volumetry can additionally he applied. These techniques relied on formula such as height x width x length x jt/6 to calculate approximate tumor volume or determined the volume hy integration of the individual slice volumes (Fig. 7.14). 

The data volume, which can be imported as data block or single slices, can be cutted or rebinned (e.g. if the data set is very large) and interpolated (e.g. interpolating intermediate slices between measured CT cuts in the case of 2D-CT). 

With 3D-CTVicwer the export of slice-contours from parts inside the data volume is possible via the DXF-format. From these contours a two-dimensional comparison to the CAD geometry is possible if the coordinate system and the absolute scaling between both methods are well known. 

Figure 9.10 Three-dimensional representation of the data volume of a tryptic digest of ovalbumin. Series of planar slices through the data volume produce stacks of disks in order to show peaks. Reprinted from Analytical Chemistry, 67, A. W. Moore Jr and J. W. Jorgenson, Comprehensive three-dimensional separation of peptides using size exclusion chromatogra-phy/reversed phase liquid chromatography/optically gated capillary zone electrophoresis, pp. 3456-3463, copyright 1995, with permission from the American Chemical Society.

Imagine an emulsion formed of suspended particles all exactly alike, and contained in a vertical cylinder of unit cross-section. The state of a horizontal slice contained between the levels h and h - - dh would not be changed if we enclosed it between two semipermeable pistons which allow the molecules of water to pass, but stop those of the gamboge. Each piston experiences an osmotic pressure, by reason of its bombardment by gamboge particles, and if there are n particles per unit volume at height h... 

In our case, detector one ( X = 254 nm) responds only to component one. Therefore, considering a chromatogram slice dt as representing hydrodynamic volumes dV ... 

Furthermore, in the more general case we are concerned with a variation of composition and sequence length distribution not only as a function of retention volume but within each chromatogram area segment (or "slice ) at each retention volume. A significant polydispcrsity of one of these properties within a chromatogram slice can easily invalidate the polymer analysis described above. 

The effect could be elucidated by ad tional axial dispersion characterization of GPC 1. An alternate approach is to utilize only THF in botii GPC 1 and 2 and to observe whether slices exit at the expected hydrodynamic volume. 

GPC 1 retention time at which chromatogram slice was obtained for GPC 2 Retention volume... 

Another approach to obtain spatially selective chemical shift information is, instead of obtaining the entire image, to select only the voxel of interest of the sample and record a spectrum. This method called Volume Selective spectroscopY (VOSY) is a ID NMR method and is accordingly fast compared with a 3D sequence such as the CSI method displayed in Figure 1.25(a). In Figure 1.25(b), a VOSY sequence based on a stimulated echo sequence is displayed, where three slice selective pulses excite coherences only inside the voxel of interest. The offset frequency of the slice selective pulse defines the location of the voxel. Along the receiver axis (rx) all echoes created by a stimulated echo sequence are displayed. The echoes V2, VI, L2 and L3 can be utilized, where such multiple echoes can be employed for signal accumulation. 

Spatially localized NMR spectroscopy was performed using a sample composed of a monoolein-D20 dispersion forming a cubic liquid-crystalline phase [41]. The spectra were selected from a slice of 300-pm thickness. The direction of the gradient was along the spinning axis. A spectral resolution was obtained that had never been observed before when selecting the whole volume of the sample. 

Fig. 2.4.3 (a) Image of a flat oil-glass interface centered along the sensitive volume. The length of the pulses was set to 5 ps to excite a slice thicker than the PSF width. The dashed line displays the step sample interface, (b) PSF obtained as the derivative of the step image shown in (a). It is symmetrical and has a linewidth of about 2.3 pm. 

Fig. 2.6.7 General principle of time-of-flight flow detection, (a) Schematic of a set-up for TOF experiments. An object of interest is placed inside an environment optimized for encoding (field gradients not shown). As the sensor medium flows out of the analyte object, its magnetization is recorded with a second coil with a smaller volume, which is placed as close to the encoding volume as possible, (b) Generic pulse sequence used for TOF experiments. Encoding along one dimension can be done by inverting the magnetization of a slice...

Fig. 5.5.7 A 2D slice through a H 3D MR image of the fixed-bed of catalyst particles. The catalyst particles appear as black fluid within the inter-particle space is indicated by lighter shades. Chemical conversion within ten selected volumes within each of the three transverse sections indicated is investigated in Figures 5.5.9-5.5.11. The direction of superficial flow (z) is also shown. Reproduced with permission from Ref. [24], copyright Elsevier (2002).

Figure 5.5.8 shows the volume selective spectroscopy pulse sequence used. This pulse sequence combines elements of NMR spectroscopy and MRI pulse sequences three slice selective rf pulses are applied in three orthogonal directions to obtain 1H spectra from pre-determined local volumes within the sample [30]. In this particular application, spectra were recorded from local volumes of dimension 1.5 mm x 1.5 mm x 0.5 mm within the fixed bed the data acquisition time for each spectrum was 3 min. Figure 5.5.9(a) shows the local volumes selected within slice 3 of the bed, as identified in Figure 5.5.7. In Figure 5.5.9(b) the 1H spectra recorded from within these volumes are shown data are presented only for the range of... 

Fig. 5.5.9 Volume selective spectroscopy within the fixed-bed reactor, (a) The location of the ten selected volumes within image slice 3 (see Figure 5.5.7) are identified, (b) It is clearly seen that the chemical shifts of peak B obtained from the spectra recorded from the selected volumes occur at significantly different values...

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