scholarly journals Tractography in Curvilinear Coordinates

2021 ◽  
Vol 15 ◽  
Author(s):  
Uzair Hussain ◽  
Corey A. Baron ◽  
Ali R. Khan
Keyword(s):  
Medical Imaging ◽  
Sensitivity And Specificity ◽  
Curvilinear Coordinates ◽  
Spherical Coordinates ◽  
Coordinate Systems ◽  
Cartesian Coordinates ◽  
Diffusion Tractography ◽  
Specificity And Sensitivity ◽  
Physical Laws ◽  
Coordinate Invariance

Coordinate invariance of physical laws is central in physics, it grants us the freedom to express observations in coordinate systems that provide computational convenience. In the context of medical imaging there are numerous examples where departing from Cartesian to curvilinear coordinates leads to ease of visualization and simplicity, such as spherical coordinates in the brain's cortex, or universal ventricular coordinates in the heart. In this work we introduce tools that enhance the use of existing diffusion tractography approaches to utilize arbitrary coordinates. To test our method we perform simulations that gauge tractography performance by calculating the specificity and sensitivity of tracts generated from curvilinear coordinates in comparison with those generated from Cartesian coordinates, and we find that curvilinear coordinates generally show improved sensitivity and specificity compared to Cartesian. Also, as an application of our method, we show how harmonic coordinates can be used to enhance tractography for the hippocampus.

Representation of Reservoir Geometry for Numerical Simulation

1970 ◽  
Vol 10 (04) ◽  
pp. 393-404 ◽  
Author(s):  
G.J. Hirasaki ◽  
P.M. O'Dell
Keyword(s):  
Coordinate System ◽  
Curvilinear Coordinates ◽  
Reference Plane ◽  
Cartesian Coordinate System ◽  
Curvilinear Coordinate System ◽  
Coordinate Systems ◽  
Cartesian Coordinates ◽  
Curvilinear Coordinate ◽  
Reservoir Geometry ◽  
Cartesian Coordinate

Abstract For most reservoirs the reservoir thickness and dip vary with position. For such reservoirs, the use of a Cartesian coordinate system is awkward as the coordinate surfaces are planes and the finite-difference grid elements are rectangular parallepipeds. However, these reservoirs may be efficiently parallepipeds. However, these reservoirs may be efficiently modeled with a curvilinear coordinate system that has coordinate surfaces that coincide with the reservoir surfaces. A procedure is presented that may be used to determine a curvilinear coordinate system that will conform with the geometry of the reservoir. The reservoir geometry is described by the depth of the top of the reservoir and the thickness. The mass conservation equations are presented in curvilinear coordinates. The finite-difference equations differ from the usual Cartesian coordinate formulation by a factor multiplying the pore volume and transmissibilities. A numerical example is presented to illustrate the magnitude of the error that may occur in the computed oil recovery if the Cartesian coordinate system is simply modified to yield the correct depth and pore volumes. Introduction Many reservoirs have a shape that is inconvenient and possibly inaccurate to model with Cartesian coordinates. The use of a curvilinear coordinate system that follows the shape of the reservoir can be advantageous for such reservoirs. The formulation discussed here will have the greatest advantage in modeling thin reservoirs but will have little advantage in modeling a reservoir whose thickness is greater than its radius of curvature, such as a pinnacle reef. pinnacle reef. In this paper the reader is introduced to various grid systems used to model reservoirs. A brief discussion of some concepts of differential geometry contrasts differences between Cartesian coordinates and curvilinear coordinates. A curvilinear coordinate system for modeling reservoir geometry is presented. Formulation of the conservation equations in curvilinear coordinates and the necessary modifications to pore volume and transmissibility are discussed. A numerical example illustrates the magnitude of the error that may result from some coordinate systems. COORDINATE SYSTEMS AND RESERVOIR GRID NETWORKS A reservoir is usually described with the depth, thickness, boundaries, etc., shown on a structure map with sea level as a reference plane. For example, the subsea depth may be shown as a contour map on the reference plane with a Cartesian coordinate grid superimposed on the reference plane as shown on Fig. 1. The Cartesian coordinates, plane as shown on Fig. 1. The Cartesian coordinates, (y1, y2), have been defined as the coordinates for the reference plane. If the reservoir surfaces are parallel planes, Cartesian coordinates may be used. The Cartesian coordinate may be rotated such that the coordinate surfaces coincide with the reservoir surfaces. SPEJ P. 393

Equilibrium and diffusion equations using cylindroidal coordinates

2002 ◽  
Vol 216 (1) ◽  
pp. 61-72 ◽  
Author(s):  
D B Dooner
Keyword(s):  
Diffusion Equation ◽  
Equilibrium Equation ◽  
Curvilinear Coordinates ◽  
Diffusion Equations ◽  
Spherical Coordinates ◽  
Cartesian Coordinates ◽  
And Diffusion

Presented is a system of curvilinear coordinates based on a cylindroid. Cartesian, cylindrical and spherical coordinates are special scenarios that emerge from a system of cylindroidal coordinates. A system of cylindroidal coordinates was originally proposed to parameterize toothed bodies or generalized hyperboloidal gear elements, and consequently certain fundamental relations for conjugate hyperboloidal pitch surfaces in mesh are presented. Two applications of cylindroidal coordinates are presented. The first application addresses the equilibrium equation and the second application addresses the diffusion equation for a differential cylindroidal element. It is demonstrated that the developed diffusion equation degenerates into established diffusion relations for cylindrical, spherical and Cartesian coordinates.

Numerical Simulation of Single Drops in a Vertical Pipe Using Various Coordinate Systems

2007 ◽  
Author(s):  
Keishun Hirokawa ◽  
Kosuke Hayashi ◽  
Akira Sou ◽  
Akio Tomiyama ◽  
Naoki Takada
Keyword(s):  
Spatial Resolution ◽  
Velocity Ratio ◽  
Three Dimensional ◽  
Terminal Velocity ◽  
Continuous Phase ◽  
Curvilinear Coordinates ◽  
Coordinate Systems ◽  
Vertical Pipe ◽  
Cylindrical Coordinates ◽  
Cartesian Coordinates

The effects of the diameter ratio λ (= d/D, where d and D are the diameters of a drop and a pipe, respectively), the Morton number M and the viscosity ratio κ (= μd/μc, where μ is the viscosity and the subscripts d and c are the dispersed fluid particle and the continuous phase, respectively) on terminal velocities and shapes of single drops rising through stagnant liquids in a vertical pipe are investigated experimentally. Then, the drops in the pipe are simulated using a volume tracking method with various coordinate systems, i.e., three-dimensional (3D) cylindrical coordinates, 3D general curvilinear coordinates and 3D Cartesian coordinates. Predicted velocities and shapes of the drops using three coordinate systems are compared with the measured data to examine the effects of coordinate systems on the accuracy of prediction. As a result, (1) The velocity ratio VT/VT0 (VT and VT0 are the terminal velocity in a pipe and infinite liquid, respectively) decreases as λ increases, and it depends not only on λ but also on M and κ, (2) Good predictions for the terminal velocities and shapes of drops are obtained not only with cylindrical coordinates and curvilinear coordinates but also with Cartesian coordinates, provided that the spatial resolution is high, (3) When the spatial resolution is low, effects of coordinate systems on a drop shape are larger for Cartesian coordinate systems than for cylindrical coordinate and general curvilinear coordinate systems, and (4) Errors in predicted drop velocities are not so large even with very low spatial resolution.

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Diffusion equations in curvilinear coordinates

1991 ◽  
Vol 56 (3) ◽  
pp. 602-618
Author(s):  
Vladimír Kudrna
Keyword(s):  
Heat Transfer ◽  
Mass Transport ◽  
Probability Density ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Curvilinear Coordinates ◽  
Diffusion Equations ◽  
Parabolic Partial Differential Equations ◽  
Spherical Coordinates ◽  
Transformation Procedure

Parabolic partial differential equations used in chemical engineering for the description of mass transport and heat transfer and analogous relationship derived in stochastic processes theory are given. A standard transformation procedure is applied, allowing these relations to be generally written in curvilinear coordinates and particular expressions for cylindrical and spherical coordinates to be derived. The relation between the probability density for the position of a discernible particle and the concentration of a set of such particles is discussed.

scholarly journals Clock-dependent spacetime

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sung-Sik Lee
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Gravity ◽  
Hilbert Spaces ◽  
Coordinate Systems ◽  
Physical Laws

Abstract Einstein’s theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.

scholarly journals An Ensemble Feature Selection Approach to Identify Relevant Features from EEG Signals

2021 ◽  
Vol 11 (15) ◽  
pp. 6983
Author(s):  
Maritza Mera-Gaona ◽  
Diego M. López ◽  
Rubiel Vargas-Canas
Keyword(s):  
Feature Selection ◽  
Sensitivity And Specificity ◽  
Eeg Signals ◽  
Specificity And Sensitivity ◽  
Selection Approach ◽  
Feature Selection Approach ◽  
The Stability ◽  
Selection Algorithms ◽  
Epileptiform Events

Identifying relevant data to support the automatic analysis of electroencephalograms (EEG) has become a challenge. Although there are many proposals to support the diagnosis of neurological pathologies, the current challenge is to improve the reliability of the tools to classify or detect abnormalities. In this study, we used an ensemble feature selection approach to integrate the advantages of several feature selection algorithms to improve the identification of the characteristics with high power of differentiation in the classification of normal and abnormal EEG signals. Discrimination was evaluated using several classifiers, i.e., decision tree, logistic regression, random forest, and Support Vecctor Machine (SVM); furthermore, performance was assessed by accuracy, specificity, and sensitivity metrics. The evaluation results showed that Ensemble Feature Selection (EFS) is a helpful tool to select relevant features from the EEGs. Thus, the stability calculated for the EFS method proposed was almost perfect in most of the cases evaluated. Moreover, the assessed classifiers evidenced that the models improved in performance when trained with the EFS approach’s features. In addition, the classifier of epileptiform events built using the features selected by the EFS method achieved an accuracy, sensitivity, and specificity of 97.64%, 96.78%, and 97.95%, respectively; finally, the stability of the EFS method evidenced a reliable subset of relevant features. Moreover, the accuracy, sensitivity, and specificity of the EEG detector are equal to or greater than the values reported in the literature.

Specificity and Sensitivity of Hemosiderin-Laden Macrophages in Routine Bronchoalveolar Lavage in Children

2006 ◽  
Vol 130 (11) ◽  
pp. 1684-1686 ◽  
Author(s):  
Zeynep N. Salih ◽  
Afreen Akhter ◽  
Javeed Akhter
Keyword(s):  
Bronchoalveolar Lavage ◽  
Sensitivity And Specificity ◽  
Pediatric Population ◽  
Strong Association ◽  
Clinical Findings ◽  
Clinical Syndrome ◽  
Pulmonary Hemosiderosis ◽  
Specificity And Sensitivity ◽  
Long Term Prognosis

Abstract Context.—The presence of iron or hemosiderin in macrophages obtained in routine bronchoalveolar lavage is considered crucial in the diagnosis of the clinical syndrome of hemosiderosis. However, there do not appear to be any data on the sensitivity and specificity of the finding of hemosiderin-laden macrophages (HLMs) in bronchoalveolar lavage in children. Objective.—To review data from bronchoalveolar lavage studies done in children to correlate the presence of HLMs with pneumonia and hemosiderosis and to determine what proportion of HLMs has the optimal sensitivity and specificity for the diagnosis of hemosiderosis. Design.—One hundred ten bronchoalveolar lavage specimens obtained via flexible bronchoscopy were reviewed retrospectively. The data collected for demographics, indication for the bronchoscopy, diagnosis of pneumonia, anemia, and bronchoscopy and bronchoalveolar lavage findings were compared between patients diagnosed with hemosiderosis and those diagnosed with other diseases. Results.—Six patients were diagnosed with hemosiderosis by clinical findings, lung biopsy, or autopsy. There were no statistical differences in pneumonia (P > .99), anemia (P > .99), or coughing (P = .08) between patients with hemosiderosis and other patients. Hemoptysis was the only symptom that was significantly different between the 2 groups (P = .04). The mean HLM index for patients with hemosiderosis was 56% ± 16.17% and for other patients, 7.5% ± 10.74% (P < .001). A HLM index of 35% gave a sensitivity of 1% and a specificity of .96%. Conclusions.—These results confirm a strong association between HLM index and diagnosis of hemosiderosis in a pediatric population. Availability of this HLM index will result in accurate and timely diagnosis of pulmonary hemosiderosis, which may influence treatment and long-term prognosis.

scholarly journals Expression of tumor pyruvate kinase M2 isoform in plasma and stool of patients with colorectal cancer or adenomatous polyps

2019 ◽  
Author(s):  
Farideh Rigi ◽  
Aliakbar Jannatabad ◽  
Azra Izanloo ◽  
Reza Roshanravan ◽  
Hamid Reza Hashemian ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Pyruvate Kinase ◽  
Sensitivity And Specificity ◽  
Adenomatous Polyps ◽  
Plasma Samples ◽  
Proliferating Cells ◽  
Pyruvate Kinase M2 ◽  
Specificity And Sensitivity ◽  
Tumor Group ◽  
Stool Samples

Abstract Background: Tumor pyruvate kinase M2 isoform (tM2-PK), which is an isoform of PK-glycolytic enzyme and appears on the surface of cancerous proliferating cells, has been used as a diagnostic biomarker for colorectal cancer (CRC). The aim of this study was to evaluate the tM2-PK measurement test for the diagnosis of CRCs and adenomatous polyps in plasma and stool samples in an Iranian population. Methods: In this prospective study, a total of 226 stool and 178 plasma samples were received from patients referred to colonoscopy units. tM2-PK enzyme was measured using two separate ScheBo-Biotech-AG ELISA kits for stool and plasma samples. Results: At the cut-off value of 4 U/ml, in tumor group, the sensitivity of fecal tM2-PK test was 100% and the specificity was 68%, and in polyp group, the sensitivity and specificity were 87% and 68%, respectively. At the cut-off value of 15 U/ml in tumor group, the sensitivity of plasma tM2-PK test was 98% and specificity was 74% and in polyp group the sensitivity and specificity were 98% and 74%, respectively. Based on our results, a cut-off range of 4.8-8 U/ml and >8 U/ml could be used to detect polyp and tumor in stool samples, respectively. Similarly, a cut-off range of 19-25 U/ml and >25 U/ml is recommended in plasma samples for polyp and tumor detection, respectively. Conclusions: This study revealed a high specificity and sensitivity of tM2-PK test for stool and plasma samples in patients with CRC and polyps suggesting it as a non-invasive assay to diagnose CRC and adenomatous polyps.

Odontogenic Sinusitis Index (OSI)

2021 ◽  
Vol 20 (5) ◽  
pp. 58-62
Author(s):  
S. Yu. Naumov ◽  
◽  
S. A. Artyushkin ◽  
O. A. Drozdova ◽  
M. A. Aflitonov ◽  
...  
Keyword(s):  
Data Analysis ◽  
Sensitivity And Specificity ◽  
Specificity And Sensitivity ◽  
Odontogenic Sinusitis ◽  
Simple Summation

The criteria for «odontogenic sinusitis» (OS) with the highest values of specificity and sensitivity were identified. An integral odontogenicity sinusitis index (OSI) was developed based on the identified criteria. To measure the sensitivity and specificity of the criteria, a group of 261 patients was selected (113 women (43.29%), 148 men (56.70%), the average age of the patients was 36 years), consisting of 150 known to have OS and 111 patients who were known to be without OS. As a result of data analysis, the values of sensitivity and specificity were obtained for all 13 criteria. Based on the sensitivity and specificity values, all criteria were combined into an odontogenicity sinusitis index (OSI) and divided into «minor» and «major». The “large” criteria were assigned a significance point of 2, and for the “small” criteria, a significance point of 1. The determination of the odontogenic nature of sinusitis was carried out by a simple summation of the points assigned to patients during the survey, examination, and analysis of CT criteria. An odontogenic cause of sinusitis is recognized if there is a minimum of 4 points of significance, for example, one “large” (2 points) and two “small” (1 point each) criteria. The general sensitivity of the integral OSI index was 93%, the general specificity was 94%. These rates are high enough that OSI can be used to determine the «odontogenic» nature of sinusitis.

scholarly journals A-030 Sensitivity and Specificity of Measures for Dementia with Lewy Bodies

2020 ◽  
Vol 35 (6) ◽  
pp. 820-820
Author(s):  
Duarte A ◽  
Alcina J ◽  
Rodriguez M
Keyword(s):  
Sensitivity And Specificity ◽  
Lewy Body ◽  
Neuropsychological Tests ◽  
Dementia With Lewy Body ◽  
Block Design ◽  
Neuropsychological Testing ◽  
Verbal Learning ◽  
Lewy Bodies ◽  
Target Population ◽  
Specificity And Sensitivity

Abstract The present review aimed to examine sensitivity and specificity across neuropsychological tests for Dementia with Lewy Body (DLB), to enhance diagnostic utility. A systematic search of the literature was conducted. Databases used: PsycInfo, Discovery Service for Carlos Albizu University-Miami, PsycARTICLES. Data selection criteria entailed articles from 2010–2020. Search terms included: Dementia with Lewy body, sensitivity, specificity, neuropsychological assessment, neuropsychological testing. Original search yielded 27 results, from those, only 8 articles contained sensitivity and specificity regarding DLB. The target population of review were older adults 65 and older. The assessment measures analyzed were the BSID, HVLT, MMSE QSPT, SAI, MMSE, and ICS, and others. Findings of eight studies were evaluated regarding sensitivity and specificity across neuropsychological assessments for DLB. Among the most specific and sensitive measures were the Alba Screening Instrument (ASI; sensitivity 90.7%, specificity 93.6%), and a combination of the Auditory Verbal Learning Test (AVLT) percent retention, Block Design, Trail Making Test--Part A, and Benton Visual Form Discrimination (specificity 96.1% and sensitivity 88.6%). Lower specificity and sensitivity were found in Illusory contour (ICs-4; specificity and sensitivity of 37.1% and 88.6%) and the Minimental State Examination-Pentagon Test (MMSE-QSPT; specificity 78.67% and sensitivity 70.29%). Other tests and combinations were explored. Specificity ranged from 76% to 96.1%, while sensitivity ranged from 37.1% to 90.7% throughout the neuropsychological tests examined. One major limitation across the studies constituted lack of pathological, post-mortem, confirmation. Additionally, while the use of cutoff scores across assessments appeared to enhance the sensitivity and specificity, it seemed to compromise the diagnostic accuracy of AD.

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