Partial volume averaging

Potential pitfalls in the computation of CBF using deconvolution methods include patient motion and partial volume averaging, which can cause underestimation of the AIF(f). Image coregistration software to correct for patient motion and careful choice of ROIs for the AIF can minimize these pitfalls. 

Diederichs et al. (1996) applied a variant of MPR, called multiplanar volume reconstruction (MPVR), to the study of the middle ear after high-resolution computed tomography performed with a reduced dose. The aim of the study was to reduce image noise and at the same time increase the partial volume averaging to balance this effect the tentative attempt failed for visualization of little bony structures, and, for example, the stapes was not visualized. 

Spectral CT could therefore have a major impact on the clinical value of CT coronary angiography. Without beam hardening artifacts, in-stent lumens become accessible and with partial volume averaging, reduced both vessel lumens adjacent to stent struts and densely calcified plaques are more accurately dehn-eated (Feuerlein et ah 2008). Overall, two new application scenarios could be feasible one is the foUow-up of patients after percutaneous coronary interventions with stent implantation the other is the evaluation of patients with known CAD or calcified vessels. Spectral detector technology may promote CT to become the primary tool for CAD imaging (Roessl and Proksa 2007 Feuerlein et al. 2008). 

Trajectory calculations require the calculation of net force acting on the dispersed phase particles. To calculate such a net force, local values of pressure, continuous phase velocities, partial and substantial derivative of pressure and partial and substantial derivatives of continuous phase velocities need to be available at the center of mass position of dispersed particles. However, these Eulerian variables and their derivatives are known only at discrete nodes in the computational domain. Therefore, suitable interpolation should be used to obtain the required values at the particle location, using the previously obtained solution of the continuous phase flow equations. As a first-level approximation, a continuous phase velocity may be taken as a computational cell based velocity for all locations within the cell. The accuracy of the results, however, will be significantly influenced by this assumption. A better assumption would be to use appropriate area or volume averaging. The concept may be illustrated by considering a two-dimensional example as shown in Fig. 7.14. The local value of a quantity / at the center of mass of the dispersed phase particle (/p) can be calculated using... 

The volume of solute is the product of its mass Jt by the (average) partial volume per unit mass Wj (see Chapter 5, Section 2.1). Thus,... 

In this case we do not rely on facts observed directly but begin by designing on the basis of reasonable assumptions a model of the perfect gas on the proper choice of this model depends the success of the whole undertaking. Wc assume that both the gases enclosed in volumes V and V2 consist respectively of n and ri2 spherical atoms or molecules, of very small total volume as compared with Vi and V2 (e.g. roVir) which exert no forces on one another and behave on collision as elastic rigid spheres following the laws of classic mechanics. In each of the partial volumes these particles should execute entirely random motions at velocities w characterized by MaxwelPs law of distribution, the average value w of which can be calculated simply from the Boyle-Charles equation... 

As in the agglomerate model, the governing equations of the volume-averaged model describe the representative concentration, Cj, and the electric potential, here in the form of the overpotential, rj, via spatially distributed partial differential equations (cf, [39]). The component mass balance is identical with Eq. (28.75) ... 

The governing equations for the continuous phase of multiphase flows can be derived from the Navier Stokes equations for single-phase flows. Considering the existence of dispersed particles, a volume-averaging technique is used to develop a set of partial differential equations to describe the mass and momentum conservation of the liquid phase. The continuity equation for the liquid phase can be given as... 

In practice, the situation can be more complicated, since motions around interdependent axes might lead to complex motional patterns, or the EFG may have no axial symmetry. The resulting 2H wide/line spectrum then can exhibit a modified shape, from which further information about the geometry of motions can be obtained. 2H wide-line spectra thus contain a wealth of information about the time scales and geometries of local bond motions in systems with partial motional averaging. Order parameters are established in characterising liquid crystalline phases, particularly for lipids. Typical values of S in aggregated alkyl chains of volume phases are on the order of 0.1- 0.2. 

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