Addendum: ’’Elastic collision in one dimension viewed as a linear transformation’’

1976 ◽  
Vol 44 (11) ◽  
pp. 1137-1137
Author(s):  
Yuk Ling Yung
Keyword(s):  
Linear Transformation ◽  
Elastic Collision ◽  
One Dimension

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

Quantitative Diameter Measurements of Chromatin and TMV Fibers in the Freeze-Dried State

1988 ◽  
Vol 46 ◽  
pp. 170-171
Author(s):  
B. D. Athey ◽  
A. L. Stout ◽  
M. F. Smith ◽  
J. P. Langmore
Keyword(s):  
Reliable Method ◽  
Fiber Diameter ◽  
Quantitative Agreement ◽  
One Dimension ◽  
Fiber Axis ◽  
Two Dimensional ◽  
Fiber Density ◽  
Variable Diameter ◽  
Freeze Dried ◽  
Expected Values

Although there is general agreement that Inactive chromosome fibers consist of helically packed nucleosomes, the pattern of packing is still undetermined. Only one of the proposed models, the crossed-linker model, predicts a variable diameter dependent on the length of DNA between nucleosomes. Measurements of the fiber diameter of negatively-stained and frozen- hydrated- chromatin from Thyone sperm (87bp linker) and Necturus erythrocytes (48bp linker) have been previously reported from this laboratory. We now introduce a more reliable method of measuring the diameters of electron images of fibrous objects. The procedure uses a modified version of the computer program TOTAL, which takes a two-dimensional projection of the fiber density (represented by the micrograph itself) and projects it down the fiber axis onto one dimension. We illustrate this method using high contrast, in-focus STEM images of TMV and chromatin from Thyone and Necturus. The measured diameters are in quantitative agreement with the expected values for the crossed-linker model for chromatin structure

Effect of CT-based attenuation correction on uptake ratios in skeletal SPECT

2007 ◽  
Vol 46 (01) ◽  
pp. 38-42 ◽  
Author(s):  
V. Schulz ◽  
I. Nickel ◽  
A. Nömayr ◽  
A. H. Vija ◽  
C. Hocke ◽  
...  
Keyword(s):  
Vertebral Body ◽  
Facet Joint ◽  
One Dimension ◽  
Patient Specific ◽  
Data Sets ◽  
Facet Joints ◽  
Lumbar Vertebral Body ◽  
Ct System ◽  
Ct Data ◽  
Attenuation Corrected

SummaryThe aim of this study was to determine the clinical relevance of compensating SPECT data for patient specific attenuation by the use of CT data simultaneously acquired with SPECT/CT when analyzing the skeletal uptake of polyphosphonates (DPD). Furthermore, the influence of misregistration between SPECT and CT data on uptake ratios was investigated. Methods: Thirty-six data sets from bone SPECTs performed on a hybrid SPECT/CT system were retrospectively analyzed. Using regions of interest (ROIs), raw counts were determined in the fifth lumbar vertebral body, its facet joints, both anterior iliacal spinae, and of the whole transversal slice. ROI measurements were performed in uncorrected (NAC) and attenuation-corrected (AC) images. Furthermore, the ROI measurements were also performed in AC scans in which SPECT and CT images had been misaligned by 1 cm in one dimension beforehand (ACX, ACY, ACZ). Results: After AC, DPD uptake ratios differed significantly from the NAC values in all regions studied ranging from 32% for the left facet joint to 39% for the vertebral body. AC using misaligned pairs of patient data sets led to a significant change of whole-slice uptake ratios whose differences ranged from 3,5 to 25%. For ACX, the average left-to-right ratio of the facet joints was by 8% and for the superior iliacal spines by 31% lower than the values determined for the matched images (p <0.05). Conclusions: AC significantly affects DPD uptake ratios. Furthermore, misalignment between SPECT and CT may introduce significant errors in quantification, potentially also affecting leftto- right ratios. Therefore, at clinical evaluation of attenuation- corrected scans special attention should be given to possible misalignments between SPECT and CT.

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