Point Of Maximum Curvature Research Articles

Micro-CT evaluation of several glide path techniques and ProTaper Next shaping outcomes in maxillary first molar curved canals.

To evaluate the ability of ProGlider instruments, PathFiles and K-files to maintain canal anatomy during glide path preparation using X-ray computed micro-tomography (micro-CT). Forty-five extracted maxillary first permanent molars were selected. Mesio-buccal canals were randomly assigned (n=15) to manual K-file, PathFile or ProGlider groups for glide path preparation. Irrigation was achieved with 5% NaOCl and 10% EDTA. After glide path preparation, each canal was shaped with ProTaper Next X1 and X2 to working length. Specimens were scanned (isotropic voxel size 9.1μm) for matching volumes and surface areas and post-treatment analyses. Canal volume, surface area, centroid shift, canal geometry variation through ratio of diameter ratios and ratio of cross-sectional areas were assessed in the apical and coronal levels and at the point of maximum canal curvature. One-way factorial anovas were used to evaluate the significance of instrument in the various canal regions. Post-glide path analysis revealed that instrument factor was significant at the apical level for both the ratio of diameter ratios and the ratio of cross-sectional areas (P<0.001), with an improved maintenance of root canal geometry by ProGlider and PathFile. At the coronal level and point of maximum canal curvature, ProGlider demonstrated a tendency to pre-flare the root canal compared with K-file and PathFile. PathFile and ProGlider demonstrated a significantly lower centroid shift compared with K-file at the apical level (P=0.023). Post-shaping analysis demonstrated a more centred preparation of ProGlider, compared with PathFile and K-files, with no significant differences for other parameters. Use of ProGlider instruments led to less canal transportation than PathFiles and K-files.

Determining the Mechanical Characteristics of Microspheres in Compression

The methodology to determine the compressive strength of microspheres is improved. It is validated by buoyancy measurements. It is demonstrated that the tangent circle method allows determining the point of maximum curvature of the stress–strain curve of microspheres. The optimal ratio of the height of microspheres to the diameter of the die mold (H/D) is determined. Curves of variation of the elastic modulus and absorbed strain energy with the maximum cyclic stress are plotted.

Surface tension-induced stress concentration around an elliptical hole in an anisotropic half-plane

We examine the surface tension-induced stress concentration around an elliptical hole inside an anisotropic half-plane with traction-free surface. Using conformal mapping techniques, the corresponding complex potential in the half-plane is expressed in a series whose unknown coefficients are determined numerically. Our results indicate that the maximum hoop stress around the hole (which appears in the vicinity of the point of maximum curvature) increases rapidly with decreasing distance between the hole and the free surface. In particular, for an elliptical or even circular hole in an anisotropic half-plane we find that, with decreasing distance between the hole and the free surface, the hoop stress can switch from compressive to tensile at certain points on the hole's boundary and from tensile to compressive at others. This phenomenon is absent in the case of an elliptical or even circular hole in the corresponding case of an isotropic half-plane.

Electro-elastic fields around two arbitrarily-shaped holes in a finite electrostrictive solid

Stress and electric field concentration around two arbitrarily-shaped holes in a finite electrostrictive solid subjected to uniform remote electric field are studied. The edge of the solid and the shapes of the holes are defined via several conformal mappings. The electro-elastic field of the solid as well as the electric fields both outside the solid and inside the holes are obtained on using conformal mapping techniques, Faber series and Fourier expansion method. Extensive numerical results are shown for elliptical, triangular, square, oval and rectangular holes in a square electrostrictive plane. The exact external electric field near the edge of the solid is found to be essentially non-uniform and its maximum appears to be much larger than the uniform remote electric field, while it is shown that the hoop stress nearby the point of maximum curvature on the hole's boundary increases rapidly as the point of maximum curvature approaches either the edge of the solid or the other hole. On the other hand, for a single centrally-located hole, the finite electrostrictive plane can be approximately treated as an infinite plane if the size of the finite plane is not less than six times the size of the hole, while for two interacting holes, the interaction between them is negligible when the distance between the two holes is larger than three times the size of the holes.

Determination of the Thickness of a Resistive Material Layer in a Finite Volume Conductor using Focused Impedance Method (FIM) – a simulation study

Focused Impedance Method (FIM) is an innovative and relatively new electrical impedance measurement technique that allows localized measurement of the properties of electrically conducting materials in a volume conductor such as the human body using simple measurement setups. In a previous work, FIM, with dual electrode separation, was used to determine thicknesses of subcutaneous fat layers through experimental study on phantoms and human subjects. The present work, carried out using COMSOL Multiphysics software package, is a finite element simulation study for a similar target object that verifies and extends the results of the previous experimental work. A rectangular box of different heights containing a material of uniform conductivity such as saline together with internally embedded layers of resistive materials of different thicknesses were used for this study. The measured transfer impedance in the FIM method showed marked change with the variation of the thickness of the resistive layer and with electrode separation, showing a point of maximum curvature in the latter. We obtained a calibration curve for the thickness from the electrode separation of this point. This allowed a unique method for the determination of thickness of embedded resistive layers which is more general than what had been done in the previous experimental work. This work will help standardize the application of 4-electrode FIM for determination of the thickness of less-conducting material layer in any finite volume, including determination of fat layer thickness, etc.Bangladesh Journal of Medical Physics Vol.7 No.1 2014 8-23

Micro–Computed Tomography Evaluation of ProTaper Next and BioRace Shaping Outcomes in Maxillary First Molar Curved Canals

IntroductionThe aim of this micro–computed tomography study was to describe the shaping properties of ProGlider/ProTaper Next (PG/PTN) and ScoutRace/BioRace (SR/BR) nickel-titanium rotary systems. MethodsThirty maxillary first permanent molars were selected. Mesiobuccal canals were randomly assigned (n = 15) to PG/PTN or SR/BR groups. Irrigation was performed with 5% NaOCl and 10% EDTA. Specimens were scanned (voxel size, 9.1 μm) for matching volumes and surface areas and post-treatment analyses. Root canal centering ability, canal geometry enlargement, and thickness of dentinal wall at inner curvature were assessed at apical level and point of maximum curvature. Results were analyzed with 4 one-way analyses of variance. ResultsCanal centering ability was superior in PG/PTN (P = .006 at apical level, P = .025 at point of maximum curvature). PG/PTN demonstrated a more conservative increase of canal areas (P = .027 at apical level, P = .038 at point of maximum curvature). Centrifugal increase in canal diameters did not significantly differ between groups (P = .65 at apical level, P = .61 at point of maximum curvature). Inner dentinal wall thickness was less reduced with PG/PTN compared with SR/BR, with no statistical differences (P = .23 at point of maximum curvature, P = .89 at apical level). PG/PTN shaping taper ranged between 6% and 7%. ConclusionsNeither system produced significant shaping errors in curved canals. PG/PTN system showed better preservation of canal anatomy. PTN offset section did not influence final preparation taper.

Variations of the blood gas levels and thermodilutional parameters during ICP monitoring after severe head trauma in children.

The purpose of this study was to define, in children following head trauma and GSC ≤ 8, at which level of intracranial pressure (ICP), the thermodilutional, and gas analytic parameters implicated in secondary cerebral insults shows initial changes. We enrolled in the study 56 patients: 30 males and 26 females, mean age 71 ± 52 months. In all children, volumetric hemodynamic and blood gas parameters were monitored following initial resuscitation and every 4 h thereafter or whenever a hemodynamic deterioration was suspected. During the cumulative hospital stay, a total of 1050 sets of measurements were done. All parameters were stratified in seven groups according to ICP (group A1 = 0-5 mmHg, group A2 = 6-10 mmHg, group A3 = 11-15 mmHg, group A4 16-20 mmHg, group A5 21-25 mmHg, group A6 26-30 mmHg, group A7 >31 mmHg). Mean values of jugular oxygen saturation (SJO2), jugular oxygen partial pressure (PJO2), extravascular lung water (EVLWi), pulmonary vascular permeability (PVPi), fluid overload (FO), and cerebral extraction of oxygen (CEO2) vary significantly from A3 (11-15 mmHg) to A4 (16-20 mmHg). They relate to ICP in a four-parameter sigmoidal function (4PS function with: r(2) = 0.90), inflection point of 15 mmHg of ICP, and a maximum curvature point on the left horizontal asymptote at 13 mmHg of ICP. Mean values of SJO2, PJO2, EVLWi, PVPi, FO, and CEO2 become pathologic at 15 mmHg of ICP; however, the curve turns steeper at 13 mmHg, possibly a warning level in children for the development of post head trauma secondary insult.

Tolerance for local and global differences in the integration of shape information.

Shape is a critical cue to object identity. In psychophysical studies, radial frequency (RF) patterns, paths deformed from circular by a sinusoidal modulation of radius, have proved valuable stimuli for the demonstration of global integration of local shape information. Models of the mechanism of integration have focused on the periodicity in measures of curvature on the pattern, despite the fact that other properties covary. We show that patterns defined by rectified sinusoidal modulation also exhibit global integration and are indistinguishable from conventional RF patterns at their thresholds for detection, demonstrating some indifference to the modulating function. Further, irregular patterns incorporating four different frequencies of modulation are globally integrated, indicating that uniform periodicity is not critical. Irregular patterns can be handed in the sense that mirror images cannot be superimposed. We show that mirror images of the same irregular pattern could not be discriminated near their thresholds for detection. The same irregular pattern and a pattern with four cycles of a constant frequency of modulation completing 2π radians were, however, perfectly discriminated, demonstrating the existence of discrete representations of these patterns by which they are discriminated. It has previously been shown that RF patterns of different frequencies are perfectly discriminated but that patterns with the same frequency but different numbers of cycles of modulation were not. We conclude that such patterns are identified, near threshold, by the set of angles subtended at the center of the pattern by adjacent points of maximum convex curvature.

The homeostatic set point of the hypothalamus-pituitary-thyroid axis--maximum curvature theory for personalized euthyroid targets.

BackgroundDespite rendering serum free thyroxine (FT4) and thyrotropin (TSH) within the normal population ranges broadly defined as euthyroidism, many patients being treated for hyperthyroidism and hypothyroidism persistently experience subnormal well-being discordant from their pre-disease healthy euthyroid state. This suggests that intra-individual physiological optimal ranges are narrower than laboratory-quoted normal ranges and implies the existence of a homeostatic set point encoded in the hypothalamic-pituitary-thyroid (HPT) axis that is unique to every individual.MethodsWe have previously shown that the dose–response characteristic of the hypothalamic-pituitary (HP) unit to circulating thyroid hormone levels follows a negative exponential curve. This led to the discovery that the normal reference intervals of TSH and FT4 fall within the ‘knee’ region of this curve where the maximum curvature of the exponential HP characteristic occurs. Based on this observation, we develop the theoretical framework localizing the position of euthyroid homeostasis over the point of maximum curvature of the HP characteristic.ResultsThe euthyroid set points of patients with primary hypothyroidism and hyperthyroidism can be readily derived from their calculated HP curve parameters using the parsimonious mathematical model above. It can be shown that every individual has a euthyroid set point that is unique and often different from other individuals.ConclusionsIn this treatise, we provide evidence supporting a set point-based approach in tailoring euthyroid targets. Rendering FT4 and TSH within the laboratory normal ranges can be clinically suboptimal if these hormone levels are distant from the individualized euthyroid homeostatic set point. This mathematical technique permits the euthyroid set point to be realistically computed using an algorithm readily implementable for computer-aided calculations to facilitate precise targeted dosing of patients in this modern era of personalized medicine.

A hepatitis C virus infection model with time-varying drug effectiveness: solution and analysis.

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes of interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time.

Surface tension-induced stress concentration around a nanosized hole of arbitrary shape in an elastic half-plane

This paper studies surface tension-induced stress concentration around a nanosized hole of arbitrary shape inside an elastic half-plane. Of particular interest is the maximum hoop stress on the hole’s boundary with relation to the point of maximum curvature and the distance between the hole and the free surface of the half-plane. The shape of the hole is characterized by a conformal mapping which maps the exterior of the hole onto the exterior of the unit circle in the image plane. On using the technique of conformal mapping and analytic continuation, the complex potentials of the half-plane are expressed in a series form with unknown coefficients to be determined by Fourier expansion method. Detailed numerical results are shown for elliptical, triangular, square and rectangular holes. Two basic conclusions are that the hoop stress increases with decreasing hole size and the maximum hoop stress generally appears nearby but not exactly at the point of maximum curvature. In addition, it is shown that the hoop stress nearby the point of maximum curvature on the hole’s boundary increases rapidly with decreasing distance between the hole and the free surface of the half-plane. On the other hand, if the distance between the hole and the free surface is more than three times the hole size, the effect of the free surface on the stress concentration around the hole is ignorable and the elastic half-plane can be treated approximately as an elastic whole plane.

Perturbation solution of two arbitrarily-shaped holes in a piezoelectric solid

This paper presents a perturbation solution to a two-dimensional problem of two arbitrarily shaped holes within an infinite piezoelectric solid subjected to uniform mechanical and electric loads at infinity. Of particular interest are the stress field and electric field around hole with relation to the distance between the two holes. The shape of each hole is characterized by a truncated mapping which can be regarded as that for an elliptical hole with a perturbation. By using the perturbation method and Faber series, both the complex potentials of the piezoelectric solid and the electric fields inside holes are expressed in a series form with unknown coefficients to be determined by Fourier expansion method. Detailed numerical results are shown for oval, elliptical, triangular and square holes. A basic conclusion is that the hoop stress and electric field strength nearby the point of maximum curvature on the hole׳s boundary increase rapidly with decreasing distance between the point of maximum curvature and the other hole. On the other hand, it is shown that the electric field inside non-elliptical hole is always non-uniform regardless of the distance between the two holes, while that inside elliptical hole tends to be uniform with increasing distance between the two holes. Additionally, if the distance between the two holes is more than four times the hole size, the interaction between the two holes is ignorable and the problem of two holes can be divided into two separate problems of only a single hole.

Stress field around an arbitrarily shaped nanosized hole with surface tension

Surface tension plays an important role in nanosized materials. In this paper, the stress field induced by surface tension around an arbitrarily shaped nanosized hole is investigated through complex variable method using truncated series, with an emphasis on the relationship between the hoop stress and the curvature of the hole’s boundary curve. Our numerical results for various shapes of holes show that maximum hoop stress always appears nearby, but not exactly at the point of maximum curvature on the hole’s boundary. Surprisingly, for elliptical holes with certain aspect ratios and typical non-elliptical holes (such as triangular, square and rectangular holes), our results show that hoop stress can even attain a local minimum (not a local maximum) or even the overall minimum at the point of maximum curvature. In particular, surface tension-induced hoop stress can be very large around nanosized holes. On the other hand, the surface tension-induced stress field is always localized for nanosized holes of arbitrary shapes and fades away with increasing distance from the hole.

Proposals of methods of oil capacity calculation

The aim of this work is to compare various methods of oil capacity calculation for surfaces containing cavities. In reference method, oil capacity was computed by summation of volumes contained in all the holes of measured surface using TalyMap software. Oil retention volume was calculated also on the basis of material ratio curve using the Svk and Sr2 parameters from Sk parameters group (areal extension of ISO 13565-2 standard). The second and third procedures were developed on the basis of rotation of material ratio curve axes. The fourth method is based on determination of point of maximum curvature of the normalized material ratio curve. It was found that in the most cases it was possible to obtain correct values of oil capacity using the Sk parameter family. However when the slope of material ratio curve in its middle part (core roughness) is small or high, the errors of oil capacity estimation may be large; up to 80%. In those cases the other methods gave better results–usually errors of oil capacity estimation were not higher than 10%; average deviations were about 5%. Determination of transition point between valleys and plateau regions as the point of maximum curvature of the normalized material ratio is recommended. The new proposals of oil capacity calculation can be used also for surfaces with cross-hatched pattern.

Integrated profiling of three dimensional cell culture models and 3D microscopy

Motivation: Our goal is to develop a screening platform for quantitative profiling of colony organizations in 3D cell culture models. The 3D cell culture models, which are also imaged in 3D, are functional assays that mimic the in vivo characteristics of the tissue architecture more faithfully than the 2D cultures. However, they also introduce significant computational challenges, with the main barriers being the effects of growth conditions, fixations and inherent complexities in segmentation that need to be resolved in the 3D volume.Results: A segmentation strategy has been developed to delineate each nucleus in a colony that overcomes (i) the effects of growth conditions, (ii) variations in chromatin distribution and (iii) ambiguities formed by perceptual boundaries from adjacent nuclei. The strategy uses a cascade of geometric filters that are insensitive to spatial non-uniformity and partitions a clump of nuclei based on the grouping of points of maximum curvature at the interface of two neighboring nuclei. These points of maximum curvature are clustered together based on their coplanarity and proximity to define dissecting planes that separate the touching nuclei. The proposed curvature-based partitioning method is validated with both synthetic and real data, and is shown to have a superior performance against previous techniques. Validation and sensitivity analysis are coupled with the experimental design that includes a non-transformed cell line and three tumorigenic cell lines, which covers a wide range of phenotypic diversity in breast cancer. Colony profiling, derived from nuclear segmentation, reveals distinct indices for the morphogenesis of each cell line.Availability: All software are developed in ITK/VTK and are available at https://vision.lbl.gov/Software/3DMorphometry.Contact: b_parvin@lbl.gov or hchang@lbl.govSupplementary information: Supplementary data are available at Bioinformatics online.

Three-dimensional Analysis of Root Canal Curvature and Direction of Maxillary Lateral Incisors by Using Cone-beam Computed Tomography

IntroductionRoot canal curvature can affect the technical quality of endodontic treatment. Prior studies measured canal curvature mainly by 2-dimensional radiography. The aim of this study was to measure the 3-dimensional (3D) root canal curvature and canal direction of maxillary lateral incisors by using cone-beam computed tomography (CBCT) and mathematical modeling. MethodsThe CBCT images of 186 maxillary lateral incisors from 110 patients were used to measure 3D root canal curvature by using V-works and kappa software. In addition, the direction of each root canal was determined by measuring the orientation of the apical one-third with respect to the coronal two-thirds. ResultsAll 186 maxillary lateral incisors were found to have canal curvature that was mainly oriented in the disto-palatal direction. The point of maximum curvature was located 0.5 mm from the root apex. ConclusionsMaxillary lateral incisors have 3D canal curvature that is maximal near the root apex, oriented in the disto-palatal direction. These CBCT analyses provide valuable information for root canal instrumentation of maxillary lateral incisors.

Prediction of Ultimate Bearing Capacity of Half-Screwed Pile by Integrated Exponential Function Model

This study fitted the measured loading-settlement curve of half-screwed pilewith least square model solution of difference form of integrated exponential functional model, and predict ultimate bearing capacity of half-screwed pile according to the fitted curve of maximum curvature point. Combined with practical engineering research, the study explored the feasibility, rationality and limitations of predicting the half-screwed single pile ultimate bearing capacity with least square model solution of difference form of integrated exponential functional model, and provided the theoretical basis for the popularization and application of the half-screwed pile.

Near Their Thresholds for Detection, Shapes Are Discriminated by the Angular Separation of Their Corners

Observers make sense of scenes by parsing images on the retina into meaningful objects. This ability is retained for line drawings, demonstrating that critical information is concentrated at object boundaries. Information theoretic studies argue for further concentration at points of maximum curvature, or corners, on such boundaries [1]–[3] suggesting that the relative positions of such corners might be important in defining shape. In this study we use patterns subtly deformed from circular, by a sinusoidal modulation of radius, in order to measure threshold sensitivity to shape change. By examining the ability of observers to discriminate between patterns of different frequency and/or number of cycles of modulation in a 2x2 forced choice task we were able to show, psychophysically, that difference in a single cue, the periodicity of the corners (specifically the polar angle between two points of maximum curvature) was sufficient to allow discrimination of two patterns near their thresholds for detection. We conclude that patterns could be considered as labelled for this measure. These results suggest that a small number of such labels might be sufficient to identify an object.

Kinetics and dynamics of heat-flow-induced birefringence in a glass: Modulation polarimetric representation

The birefringence induced by thermal stress in a quartz glass plate sample with a small temperature gradient has been measured using the modulation polarimetry technique. The stress distribution along and across the direction of the heat flow at specific points in time has been obtained, as well as its dependence on the time in specific coordinates of the heat flow. The inverse problem of transient thermoelasticity has been solved by graphical integration of experimental characteristics. The results obtained have the form of temperature dependences varying in time and space. It has been found that the dynamics of the point of maximum curvature of the temperature function T(t) is a characteristic of the thermal front during the establishment of a steady-state heat flow. It has been shown that the characteristics of relaxation of thermal stress and temperature contain information on the properties of a “heater-sample-surrounding air” system.

Optimum Plot Size for Field Trials of Taro (Colocasia esculenta)

Taro (Colocasia esculenta L. Schott) is a root crop widely grown in the Tropics. To determine the optimum plot size for taro field trials, fresh and dry weights of individual corms were collected from two field trials conducted under flooded culture and two conducted under upland culture. For a given maximum test plot with a single border row surrounding inner measured plants, all possible combinations of smaller plot sizes were investigated. A plot size was defined as a given number of adjacent plants. A strong linear relationship was found between the natural logarithm of variance of yield and the natural logarithm of plot size. Expressed on the non-log-transformed scale, the point of maximum curvature in this relationship indicates a sudden decrease in advantage to larger plot sizes and is taken as optimum. Calculating maximum curvature mathematically, optimum plot size was 21 inner plants (5.7 m2) for the second flooded trial and 18 inner plants (4.9 m2) for the second upland trial. Another method of estimating optimum plot size minimized the cost per unit of research data by using the index of degree of correlation between neighboring plots. In three of four trials, the optimum plot size ranged from 16 to 24 inner plants (4.3 to 6.5 m2). In this second method, we calculated a non-linear relationship between plot size and outer border plants to estimate the fixed and per-unit cost of a single border row surrounding the inner measured plants. Both methods of calculating optimal plot size sometimes resulted in estimates that exceeded the maximum test plot size for particular field trials, indicating limitations of each method and the importance of managing field trials to ensure uniformity across treatments. No evidence of spatial autocorrelation was found in the corm yield of taro, indicating that the two methods used were adequate in calculating optimum plot size. In addition, we conducted an analysis based on statistical power but found that plot size did not materially affect the power to detect differences between treatments. To our knowledge, this is the first report of optimum plot size for field trials of taro.