Motion correction eliminates discontinuities in parametric PET images of neuroreceptor binding
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Head movements during PET studies of cerebral neuroreceptors with positron emission tomography (PET), which are often recorded as dynamic studies over periods ranging from one to two hours, do not only lead to blurred images, but, by distorting pixel time-activity curves, may also seriously disturb the kinetic analysis. Here we report on the effect of head motion on parametric images of the distribution volume ratio (DVR) as well as on the elimination of artefacts, if the dynamic PET data are corrected for head movements. For this purpose we utilized six PET studies done with the 5HT2A-receptor ligand [18F]-altanserin. Prior to the tracer injection a transmission scan of 10 min was recorded for measured attenuation correction. During the PET scan, which was acquired in listmode for 1 h, the position of the head was monitored by a Polaris infrared motion tracking system. The listmode data were sorted into 42 time frames between 10 s and 2 min in duration. A time frame consists of 63 images of 128 128 voxels with a voxel size of 2 mm 2 mm 2.43 mm. The motion correction used the multiple acquisition frame (MAF) approach, which calculates individual attenuation files for each emission frame and its corresponding head position to avoid a misalignment between transmission and emission data. After reconstruction of attenuation corrected emission frames each image frame was realigned to match the head position of the first emission frame. Both the motion corrected and not corrected dynamic images were evaluated by the non-invasive Logan plot method to obtain parametric images of DVR. In addition, a dynamic [18F]-altanserin PET scan was simulated and affected by similar movements as seen in the human studies. In this way data without statistical noise could be analysed. DVR images of motion-affected [18F]-altanserin scans showed artefacts whose extent was dependent on the amount of movement. The artefacts were mainly located at the border of the cortical tissue, especially at the interior edge towards white matter. The artefacts exhibited as discontinuities and small spots, whose values exceeded the expected DVR values or were even negative. The discontinuities were found with movements of 4 mm and greater. Isolated spots were present even with movements of only 2 mm. The artefacts disappeared when the MAF based motion correction was applied. The observations obtained in human data could be confirmed in the simulated noise free [18F]-altanserin images confirming that the artefacts are due to motion and not to statistical noise. Whereas the native PET images look just blurred, if the patient has moved during the PET scan, parametric images of the Logan DVR, which are calculated by pixel-wise linear regression, contain severe discontinuities primarily at the cortical edge. At this location, the data used in the DVR calculation change between grey and white matter data because of the head motion. The MAF based head motion correction is able to avoid the described errors.Keywords:
Classification of discontinuities
Abstract Discontinuities are interruptions in the desirable physical structure of a weld. This article describes the types of weld discontinuities that are characteristic of the principal welding processes. Discontinuities covered are metallurgical discontinuities, discontinuities associated with specialized welding processes, and base metal discontinuities. In addition, information on the common inspection methods used to detect these discontinuities is provided.
Classification of discontinuities
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Classification of discontinuities
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Classification of discontinuities
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Classification of discontinuities
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Abstract Discontinuities that have unfavourable orientation and are continuous within overall engineering rock regions can have a dominant effect on the strength, deformability and permeability of the rock mass. The concepts of geometrical parameters of basic discontinuities and engineering discontinuities are proposed in this communication. Further, the engineering discontinuities are divided into key discontinuities and non‐key discontinuities. Within any region of the rock mass, the spacing, trace length and probability of engineering discontinuities can be estimated from the geometrical parameters of the basic discontinuities. In general, the geometrical parameters are different from those of the basic discontinuities. Finally, two examples are given to illustrate how to apply these parameters to rock engineering problems.
Classification of discontinuities
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Abstract. We construct and study methods for approximating the positions (localization) of discontinuities of the first kind of a one-dimensional function. Instead of the exact function, its approximation in and the perturbation level are known; smoothness conditions are imposed on the function outside the discontinuities. The number of discontinuities is countable, and all the discontinuities are divided into two sets: with the absolute value of the jump greater than some positive and discontinuities satisfying a smallness condition for the value of the jump. It is required to find the number of discontinuities in the first set and localize them using the approximately given function and the perturbation level. Since the problem is ill-posed, regularization algorithms should be used for its solution. Under additional conditions on the exact function, we construct regular methods for the localization of discontinuities and obtain estimates for the accuracy of localization and for the separability threshold, which is another important characteristic of the method. The order optimality of the constructed methods on classes of functions with discontinuities is established.
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Large solid material masses inevitably contain discontinuities. In many cases they occur in one or several parallel sets with individual discontinuities spaced at regular intervals. The numerical treatment of the combined effect of motion across discontinuities and deformation of the intervening intact blocks poses a formidable challenge. Two general complementary approaches are considered for stress wave interaction: explicit, in which the motions across the discontinuities and the deformation within the blocks are represented separately; and implicit, wherein a single effective medium is defined so as to deform on average like an assemblage of blocks and discontinuities. The implicit composite model admits arbitrary constitutive behavior in both the intact blocks and discontinuities, and by enforcing internal compatibility and stress equilibrium derives a super-element representing the combined anistropic behavior due to both discontinuities and continuous blocks, in close agreement with the explicit model.
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A structure with cut–outs or other discontinuities is generally considered to be more difficult to analyse than a similar structure without such features, although it is in fact less redundant. This is largely due to the special conditions which have to be introduced to allow for these discontinuities, tending to make the calculations less adaptable to routine computation . Another and very practical reason is that it is sometimes fairly easy to—dare we say it?—make a reasonable guess at the load distribution in a structure without cut–outs, whereas a much more critical approach is necessary for the treatment of structural discontinuities. Be that as it may, it will be assumed here that the structure without discontinuities, which will henceforth be termed the “original” structure, can be analysed exactly, in the sense that all the effective redundancies are taken into account. It will now be shown how these calculations may be modified to deal with the corresponding structure with discontinuities, which for this reason will be referred to as the “modified” structure.
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Abstract Strong and weak discontinuities can appear in different fields of mechanics. Some obvious examples where strong discontinuities arise are stationary and propagating cracks. This manuscript will thus discuss a geometrically nonlinear, meshindependent finite element framework for the modelling of stationary and propagating cracks in three dimensional continua. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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The space of discontinuities is one of important indexes which explains the distribution of discontinuities and also classifies quality of engineering rock mass.Unlike the traditional definition of discontinuities space,this paper points out that the distribution of discontinuities can be analyzed as long as the spaces of neighboring discontinuities are measured.It presents the four-type methods of classifying discontinuities to built the discontinuities series.It set up an ARIMA model of discontinuities space by means of theory of time series and provided methods of building and checking model.An actual case is studies to show that the ARIMA model is suitable.
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