Voxel size

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. 

Our method is demonstrated with experiments on a Bentheimer sandstone sample. The sample was prepared to be cylindrically shaped with a diameter of 2.5 cm and a length of 2.0 cm. The sample was fully saturated with de-ionized water under vacuum. We performed the CPMG imaging experiment described in the previous section to measure the magnetization intensity at 50 echoes spaced by 4.6 ms for each of 32 x 16 x 16 voxels within the field of view of 3.0 cm x 3.0 cm x 3.0 cm. The corresponding voxel size is 0.938 mm x 1.88 mm x 1.88 mm. We used 1 s of repetition time (TR) and the total imaging time was 4.3 min. 

Fig. 5.4.7 (a-c, e) Spatially resolved NMR spectra detected during AMS hydrogenation in a catalyst bed of 1-mm beads. Each spectrum corresponds to a voxel size of 2 x 0.17 x 0.33 mm3. Spectra in (a-c) correspond to the same radial position within the operating reactor and are detected in the top, middle and bottom parts of the reactor, respectively. Three spectra in (b, e) correspond to the same vertical position in the operating reactor, with the two spectra in (e) corresponding to voxels shifted by 1.3 mm to ether side of the voxel of the spectrum in (b). The two spectra in (e) are shifted vertically relative to each other for better presentation. The lower traces with narrow lines in (d, f) are experimental spectra detected for bulk neat AMS (d) and cumene (f), the upper traces in (d, f) were obtained by mathematically broadening the lines to 300 Hz. 

Fig. 36. Spectra recorded from SOL with decreasing voxel size as indicated in the T -weighted image (a), (b) (11 x 11 x 20) mm, 32 acq. (c) (9 x 9 x 18) mm, 48 acq. (c) (7 X 7 X 14) mm, 64 acq. (e) (5 x 5 x 10) mm, 80 acq. Examinations using smaller volumes provide an assessment of IMCL. Disturbing EMCL contaminations can be excluded from the voxel in this example.

In a practical implementation, the domain on which the phase volume functions are specified is typically a cubic grid of Nx x Ny x Nz voxels, which corresponds to real dimensions of Lx — hNx, Ly - hNy, and Lz — hNz, where h is the voxel size. We will further call this region of real space the computational unit cell. The relationship between the unit cell and the multiphase medium of interest depends on the absolute dimensions of the medium and on the spatial resolution at which the medium is represented (feature dimensions). The unit cell can either contain the entire medium and some void space surrounding it, as in the case of virtual granules described in Section IV.D below, or be a sample of a much larger (theoretically infinite) medium, as in the case of transport properties calculation, described in Section II.E below. 

The volume of cells is calculated as the number of voxels i belonging to each Voronoi region Vj, times the voxel volume h3, where h is voxel size. The symbol... 

The developed methodology is now used to determine a two-dimensional porosity distribution on a Bentheimer sandstone sample (KBE) saturated with oil. The sample and reference used are the same as those for one-dimensional imaging in Section 2.4.1. A two-dimensional CPMG imaging sequence is applied with field of view of 10.00 cm x 3.50cm, which gives a voxel size of 0.078 cm x 0.11 cm x 0.58 cm. The porosity distribution of the two-dimensional... 

The final demonstration of the developed methodology is to determine the three-dimensional porosity distribution of a porous media sample obtained from the subsurface. A cylindrically shaped rock sample was prepared, and is labeled MAG. The sample has a 2.54-cm diameter and is 3.90 cm in length. A bulk porosity of 0.284 was determined gravimetrically, with 5.61 g of brine solution being imbibed. The reference sample contained 0.217 g of water. The field of view was 10.0 cm x 3.0 cm x 3.0 cm, of which lengths are divided into 128x8x8. This yields voxel sizes of 0.078 cm x 0.375 cm x 0.375 cm. 

For a sample with sufficiently narrow linewidth and strong magnetic field gradient, the image resolution Ar is determined by the voxel size, Arvoxd... 

Fig. 12. The joint spin-velocity density function, p(z)P (v , -), as a function of position z for water flow in the rectangular Bentheimer sandstone sample (voxel size is 0 94 mm)...

Figure 3.84. Voxel obtained by irradiation of a mixed urethane acrylate oligomer and a urethane acrylate monomer in the presence of a mixture of benzoyl cyclohexanol and morpholino phenyl amino ketones at 780 nm using a 150-fs pulsed Ti sapphire mode-locked laser operating at 76 MHz, where light was focused by a 1.4 numerical aperture objective lens (a) scanning electronic microscopic images of the voxel and (b) longitudinal and lateral voxel size as function of the exposure time. (From Ref. [580] with permission of the American Institute of Physics.)...

For a 3D image (a z-stack of 2D slices), the voxel size in the z direction may differ from that in the x and y direction. When the particle radius in z-pixels is given by flz, the acquisition time for a 3D particle image is... 

Fig. 8.7.3 Proton images (bottom) of a phantom made from poly (acetal) (Delrin) acquired with the time-suspension pulse sequence of Fig. 8.6.2, The field of view is (5.9 mm). The sample (top) has been imaged in three dimensions at 400 MHz with a voxel size of 92 x 92 x 625(pLtti). Adapted from [Corl2] with permission from Flsevier Science.

Finally, periodic non-destructive imaging by x-ray CT is used to view redistribution of mineral mass within the heated sample, as illustrated in Figure 2. X-ray CT records changes in density within the sample as a proxy for mineral removal or redistribution, with the scanner used in this study capable of resolving down to -1/1000 of the diameter of the sample. For sample diameters of 3-5 cm used in the following study, the minimum voxel size scales to the order of 30-50 pm. This resolution is at the limits of utility in defining mass redistribution - it is adequate to define mass redistribution in samples of Berea and limestone, but not for the relatively tighter fracture in novaculite. 

The voxel size refers to the volume of tissue of the body that absorbs the excitation pulse. In simple terms, a voxel is a sample of tissue within the body that corresponds to a specific pixel on the generated image. Each MR image is made up of a number of pixels. Hence, the larger the voxel, the larger the pixels and therefore spatial resolution is reduced. 

Voxel size is dependent on slice thickness, field of view and the matrix size and is one of the most important determinants of the SNR ratio. Larger voxels have a higher SNR as they contain more protons which are producing a signal (Creasy et al. 1995). Conversely, a larger voxel will reduce the spatial resolution. The SNR is influenced by any parameter that alters the voxel size. 

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