Exponential Image

The resulting DW images has not only diffusion contrast but also T2 contrast (also known as T2 shine through ). In order to remove the T2 weighting, the DW images S is divided by the T2 image (b=0). The exponential image is easily thus derived from (7.1) as ... 

For acute stroke studies, DW images. Exponential Images, ADC maps, and T2-weighted images should be reviewed (Fig. 7.6). In lesions such as acute ischemic strokes, both the T2 and diffusion effects cause inaeased signal on the DW images, and we identify regions of... 

In animal studies, experimental middle cerebral artery occlusion is followed by ADC values 16-68% below those of normal tissue as measured at 10 min to 2 h [15-21]. Diffusion coefficients pseudonormalize (i.e., the ADCs are similar to those of normal brain tissue though the tissue is not viable) at approximately 48 h and are elevated thereafter. In humans, the time course is longer (Table 7.2) (Fig. 7.7). Decreased diffusion in ischemic brain tissue is observed as early as 11 min after vascular occlusion [22-26]. The ADC continues to decrease with peak signal reduction at 1 days. This decreased diffusion is markedly hyperintense on DW images (a combination of T2 and diffusion weighting), less hyperintense on exponential images, and hypointense on ADC... 

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].)...

In its most common mode of operation, STM employs a piezoelectric transducer to scan the tip across the sample (Figure 2a). A feedback loop operates on the scanner to maintain a constant separation between the tip and the sample. Monitoring the position of the scanner provides a precise measurement of the tip s position in three dimensions. The precision of the piezoelectric scanning elements, together with the exponential dependence of A upon c/means that STM is able to provide images of individual atoms. 

F clean surface. The picture has been prepared merging all the individual simulated images together (evaluated at the same density contour value, i.e., 0.359 x 10 7eA 3) and allowing an exponential decay of half a simulation cell toward the clean surface value whenever the simulation cell has been found too small to allow a full recovery of the clean surface baseline. (Reprinted with permission from Ref. [3].)... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

Fig. 4.9. Schematic of time-resolved fluorescence anisotropy sample is excited with linearly polarized light and time-resolved fluorescence images are acquired with polarization analyzed parallel and perpendicular to excitation polarization. Assuming a spherical fluorophore, the temporal decay of the fluorescence anisotropy, r(t), can be fitted to an exponential decay model from which the rotational correlation time, 6, can be calculated.

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