Voxel

Finally, by volumetric imaging Three-dimensional information was obtained by stacking reflection tomograms from multiple planes. Using this stacking technique, cubic voxels were obtained and could be numerically dissected in any plane. Although there are several attractive features related to this technique, there are also several questions which need to be addressed before it can be used for industrial applications. For example, the applied sound field must be further characterized. 

At the end of the procedure the 3D voxels array represents the volume attenuation distribution of the examined objeet. Examination of the object may done by choosing for presentation of different layers in any direction of this 3D matrix with no additional exposures or computations. 

After the summation of 180° rotation, the 3D voxels array was viewed from 4 different directions. These horizontal cuts (line 20, line 50 and line 80), and a vertical cut are presented in Figs. 5 and 6. 

Figure 6. Tomographic vertical cut from the 3D voxel array of object no. 1...

Tomographic cuts obtained from the generated 3D voxel array are presented in figure 8 and 9. 

The study presented a new tomographic method based on 3D reconstruction from a single 180 exposure. The method is based on the summation principle and the 3D voxel image is generated almost in real-time. 

An extension of these metliods to 3D is the Feldkamp algorithm [7], a standard in 3D-tomographic reeonstruction today. In this case off-midplane voxels are taken into eonsideration through weighted filtered 3D-baekprojection. llie weighting compensates for the longer way an oblique ray has to travel. 

Motion, and in particular diffiision, causes a further limit to resolution [14,15]. First, there is a physical limitation caused by spins diflfiising into adjacent voxels durmg the acquisition of a transient. For water containing samples at room temperature the optimal resolution on these grounds is about 5 pm. However, as will be seen in subsequent sections, difhision of nuclei in a magnetic field gradient causes an additional... 

Figure Bl.14.6. J -maps of a sandstone reservoir eore whieh was soaked in brine, (a), (b) and (e), (d) represent two different positions in the eore. For J -eontrast a saturation pulse train was applied before a standard spin-eeho imaging pulse sequenee. A full -relaxation reeovery eiirve for eaeh voxel was obtained by inerementing the delay between pulse train and imaging sequenee. M - ((a) and (e)) and r -maps ((b) and (d)) were ealeulated from stretehed exponentials whieh are fitted to the magnetization reeovery eurves. The maps show the layered stnieture of the sample. Presumably -relaxation varies spatially due to inliomogeneous size distribution as well as surfaee relaxivity of the pores. (From [21].)...

The extension of the voxel in a radial direction gives infomiation on the lateral resolution. Since the lateral resolution has so far not been discussed in temis of the point spread function for the conventional microscope, it will be dealt with here for both conventional and confocal arrangements [13]. The radial intensity distribution in the focal plane (perpendicular to the optical axis) in the case of a conventional microscope is given by... 

In scanning mode the sequential detection of single pixels (picture elements) and voxels (volume elements) results in long measurement times in practice, therefore, only small volumes (10 x 10 x 1 p,m ) can be measured [3.56]. 

Figure 7.7. A finite element model of a bone specimen in compression. This model was created by converting the voxels from a microcomputed tomography scan into individual bone elements. Loads can then be applied to the model to understand the stresses that are created in the bone tissue.

It should be noted that, in two of these studies, " the perfusion parameter used to define the mismatch was not CBF or MTT, but instead the time it took for contrast concentration to reach peak concentration in each image voxel after contrast injection ( time to peak or TTP). TTP measurements are often used as rough approximations of MTT measurements because calculation of CBF and MTT are somewhat complex, requiring a mathematical process called deconvolution. The details of deconvolution are beyond the scope of this chapter, and the reader is referred to other sources for further explanation. In many clinical settings, maps of parameters like TTP that do not require deconvolution may be available much more quickly than those that do require deconvolution. TTP is less specific than MTT in detecting underperfused tissue because it does not distinguish between delayed contrast arrival time (such as that related to perfusion via collateral vessels) and truly prolonged intravascular transit time. 

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. 

Another type of flow artifact is due to voxel inflow and outflow problems large velocities make a spin leave its designated voxel in the time between signal encoding and signal readout. As the traveled distance d and the velocity v are related by the expression d = vt, it is obvious that the effect is more severe, the smaller the voxel size is. Slow velocities, on the other hand, may be masked by diffusive displacements. 

The second experiment covers the velocity range between the minimum measurable velocity and the minimum velocity detected by the first experiment. It is distorted because of back-folding of high velocities into the spectrum, but it shows the small velocities properly. All voxels from the first map that show zero velocity can now be compared with the corresponding (undistorted) voxels of the second map. If those show a finite velocity, the value can be transferred to the first map. 

Smaller pore sizes require a better spatial resolution, i.e., smaller voxels, which in turn conflict with a good signal-to-noise ratio. Moreover, field distortions at material boundaries then become more significant and even spins with moderate velocities will leave their designated voxel in the time between phase encoding and signal readout. 

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