Coordinates Of Tip Research Articles

The dental arch form revisited.

Recently, the beta function has been shown to be an accurate mathematical model of the human dental arch. In this research, we tried to find the equation of a curve that would be similar to the generalized beta function curve and at the same time could represent tapered, ovoid, and square dental arches. A total of 23 sets of naturally well-aligned Class I casts were selected, and the depths and widths of the dental arches were measured at the canine and second molar regions. Using the mean depths and widths, functions in the form of Y = AXm + BXn were calculated that would pass through the central incisors, canines, and second molars. Each function was compared with the generalized beta function with the use of root mean square values. It was shown that the polynomial function Y = AX6 + BX2 was the nearest to the generalized beta function. Then the coordinates of the midincisal edges and buccal cusp tips of each dental arch were measured, and the correlation coefficient of each dental arch with its corresponding sixth order polynomial function was calculated. The results showed that the function Y = AX6 + BX2 could be an accurate substitute for the beta function in less common forms of the human dental arch.

Displacement of breast tissue and needle deviations during stereotactic procedures.

The aim of this study was to quantify the displacement of breast tissue and the inaccuracy of needle positioning for biopsy (14-gauge) and localization (19.5-gauge) needles. For displacement of breast tissue, differences between the coordinates of identifiable microcalcifications in the images before (baseline) and after needle positioning were analyzed (n = 52). For accuracy of needle positioning, differences between the coordinates of the needle tip and the target were analyzed in breast tissue (n = 97) and in air (n = 246). Average target displacement was 2.1 mm for biopsy needles (95% prediction interval [PI] 0.6-7.8) and 1.0 mm (95% PI 0.3-3.9) for localization needles. Mean inaccuracy of needle positioning in breast tissue was 1.1 mm (95% PI 0.4-3.0) and 1.8 mm (95% PI 0.7-4.6) for biopsy and localization needles, respectively. Tissue and needle displacements cause a total positioning error of 2.4 mm in stereotactic core biopsy, which will limit the attainable diagnostic accuracy.

An algorithm for automatic needle localization in ultrasound-guided breast biopsies.

An algorithm was developed in order to reduce operator dependence in ultrasound-guided breast biopsy, by automatically locating the needle in the ultrasound image, and displaying its location on the image for the user. Ultrasound images of a typical breast biopsy needle inserted in a tissue-mimicking agar were obtained to test the algorithm. The resulting images were examined by a group of observers who recorded the values of the angle, intercept and tip coordinates of the needle in the image, and inter- and intra-observer variability studies were performed on the results. The results of the algorithm segmentation were compared to the values recorded by the observers, and physical measurements recorded at the time the images were acquired. The algorithm segmentation was precise enough to successfully (when considering angle and tip segmentation) target 90% of tumors of 4.5 mm in diameter situated at the center of the image.

Modification and application of a Pelorus Mark III stereotactic system for CT-guided brain biopsy in 50 dogs.

The Pelorus Mark III Stereotactic System is a commercially available device for CT-guided stereotactic brain biopsy in people. With relatively minor modifications, this device was used to safely and accurately perform CT-guided stereotactic brain biopsies in 50 dogs with intracranial lesions. Modifications were necessary to accommodate a 90 degree shift in orientation of the canine head compared to the human head during the imaging phase of the procedure, and to facilitate other phases of the biopsy procedure that are affected by the uneven and variable topography of the canine skull. Description of a typical CT-guided brain biopsy procedure in dogs using the modified Pelorus Mark III Stereotactic System is provided. Accuracy of biopsy needle placement was determined by comparing the x, y and z coordinates of the biopsy target site with the actual coordinates of the needle tip on CT images. Mean needle placement error was 3.5 +/- 1.6 mm. Needle placement error was not significantly related to operator experience, dog size (body weight), or needle path length, however, needle placement error was significantly affected by lesion location.

Three-dimensional dental arch curvature in human adolescents and adults

The three-dimensional arrangement of dental cusps and incisal edges in human dentitions has been reported to fit the surface of a sphere (the curve of Monson), with a radius of about 4 inches in adults. The objective of the current study was to compare the three-dimensional curvature of the mandibular dental arch in healthy permanent dentitions of young adults and adolescents. The mandibular casts of 50 adults (aged 19 to 22 years) and 20 adolescents (aged 12 to 14 years) with highly selected sound dentitions that were free from temporomandibular joint problems were obtained. The three coordinates of cusp tips excluding the third molars were digitized with a three-dimensional digitizer, and used to derive a spherical model of the curvature of the occlusal surfaces. From the best interpolating sphere, the radii of the left and right curves of Spee (quasi-sagittal plane) and of molar curve of Wilson (frontal plane) were computed. Mandibular arch size (interdental distances) was also calculated. The occlusal curvature of the mandibular arch was not significantly influenced by sex, although a significant effect of age was found (Student t , P < .005). The radii of the overall sphere, right and left curves of Spee, and curve of Wilson in the molar area were about 101 mm in adults, and about 80 mm in adolescents. Arch size was not influenced by either sex or age. The different curvatures of the occlusal plane in adolescents and adults may be explained by a progressive rotation of the major axis of the teeth moving the occlusal plane toward a more buccal position. These dental movements should be performed in a frontal plane on an anteroposterior axis located next to the dental crown. (Am J Orthod Dentofacial Orthop 1999;115:401-5)

Locating the crack tip of a surface-breaking crack Part I. Line crack

Four distinct algorithms to locate the crack tip of a surface-breaking crack using only the arrival time information of the first diffracted waves are described and compared. To illustrate these algorithms, a line crack in a half-plane is considered. The first two algorithms are based mainly on elementary geometric arguments, where the crack tip is formulated as the intersecting point of two ellipses (algorithm 1) and/or three circles (algorithm 2). The other two algorithms are formulated as optimization problems, where cost functions based upon the arrival time data of diffracted waves are constructed. The unknown crack tip coordinates are then determined by minimizing the cost functions through the Lagrange multiplier method (algorithm 3) or the simplex method (algorithm 4). In the numerical experiments, the exact arrival times are superimposed by Gaussian error with different levels to simulate the real extracted arrival times from experimental signals. The numerical optimization method (algorithm 4) is found to have the best performance with respect to noise, as well as for accuracy. Moreover, the recovery of the crack length is much more robust than the orientation and depth.

Mixed-mode steady-state crack growth in elastic-plastic solids

In this paper, steady, quasi-static crack growth under plane strain conditions in an elastic-plastic material subjected to mixed-mode loading (combined mode I and mode II) is analyzed. A modified small scale yielding formulation ( Journal of the Mechanics and Physics of Solids, 1993, 41, 835–861) wherein the elastic K-field as well as the T-stress are prescribed as remote boundary conditions is used. A special finite element procedure based on moving crack tip coordinates is employed to simulate steady-state crack growth in the direction ahead of the tip. The material is assumed to obey the J 2 flow theory of plasticity, with a power-law hardening stress-strain response. The results show that the near-tip mode-mixity is dependent on the level of strain hardening, magnitude and sign of the T-stress and on the remote elastic mixity. The influence of the above parameters on the near-tip stress and deformation fields is examined and the range of remote elastic mixity that gives rise to a mode I or mode II distribution is identified.

Transformation of images of defects in scanning systems of nondestructive testing

We present an analytical form corresponding to realization of the scanning principle in scanning systems of nondestructive testing. We used the form for carrying out some transformations of images of defects with recalculation of coordinates of tips of rectangles which approximate the image of a defect.

Statistical evaluation of Monson's sphere in healthy permanent dentitions in man

The three-dimensional curvature of the mandibular dental arch was studied in 20 men and 20 women with sound dentitions and free from temporomandibular joint problems. The x, y, z coordinates of cusp tips of all but the third molars were obtained with a three-dimensional digitizer, and used to derive a spherical model of the curvature of the occlusal surfaces. From the best interpolating sphere the radii of the left and right curves of Spee (quasi-sagittal plane) and of the canine and molar curves of Wilson (frontal plane) were computed. The occlusal curvature of the mandibular arch was not significantly influenced by gender, even if, on average, all the computed variables were larger in men than women. The radii of the overall sphere, right and left curves of Spee, and curve of Wilson in the molar area were about 105 mm in men, and about 100 mm in women. A relatively large intrasample variability in arch curvature was found. The mean sphere radius in men was very close to the classical value of 4 in, confirming Monson's observations, but the relatively large intrasample variability prevented any definitive determination of a sexual dimorphism in the three-dimensional characteristics of occlusal curvature.

Feasibility Study of Magnetic Resonance Imaging-Guided Intranasal Flexible Microendoscopy

Interventional magnetic resonance imaging (MRI) offers potential advantages over conventional interventional modalities such as X-ray fluoroscopy, ultrasonography, and computed tomography (CT). In particular, it does not use ionizing radiation, can provide high-quality images, and allows acquisition of oblique sections. We have carried out a feasibility study on the use of interventional MRI to track a flexible microendoscope in the paranasal sinuses. In this cadaver study, high-speed MRI was used to track a passive marker attached to the end of the endoscope.Automatic image registration algorithms were used to transfer the coordinates of the endoscope tip into the preoperative MRI and CT images, enabling us to display the position of the endoscope in reformatted orthogonal views or in a rendered view of the preoperative images. The endoscope video images were digitized and could be displayed alongside an approximately aligned, rendered preoperative image. Intraoperative display was provided in the scanner room by means of an liquid crystal display (LCD) projector. We estimate the accuracy of the endoscope tracking to be approximately 2 mm.

Feasibility study of magnetic resonance imaging-guided intranasal flexible microendoscopy.

Interventional magnetic resonance imaging (MRI) offers potential advantages over conventional interventional modalities such as X-ray fluoroscopy, ultrasonography, and computed tomography (CT). In particular, it does not use ionizing radiation, can provide high-quality images, and allows acquisition of oblique sections. We have carried out a feasibility study on the use of interventional MRI to track a flexible microendoscope in the paranasal sinuses. In this cadaver study, high-speed MRI was used to track a passive marker attached to the end of the endoscope. Automatic image registration algorithms were used to transfer the coordinates of the endoscope tip into the preoperative MRI and CT images, enabling us to display the position of the endoscope in reformatted orthogonal views or in a rendered view of the preoperative images. The endoscope video images were digitized and could be displayed alongside an approximately aligned, rendered preoperative image. Intraoperative display was provided in the scanner room by means of an liquid crystal display (LCD) projector. We estimate the accuracy of the endoscope tracking to be approximately 2 mm.

Application of stereo vision to three-dimensional deformation analyses in fracture experiments

Based on a pinhole camera model, camera model equations that account for the radial lens distortion are used to map three-dimensional (3-D) world coordinates to two-dimensional (2-D) computer image coordinates. Using two cameras to form a stereo vision, the 3-D information can be obtained. It is demonstrated that such stereo imaging systems can be used to measure the 3-D displacement field around the crack tip of a fracture specimen. To compare with the available 2-D theory of fracture mechanics, the measured displacement fields expressed in the world coordinates are converted, through coordinate transformations, to the displacement fields expressed in specimen crack tip coordinates. By using a smoothing technique, the in-plane displacement components are smoothed and the total strains are obtained. Rigid body motion is eliminated from the smoothed in-plane displacement components and unsmoothed out-of-plane displacement. Compared with the theoretical elastic-plastic field at a crack tip, the results appear to be consistent with expected trends, which indicates that the stereo imaging system is a viable tool for the 3-D deformation analysis of fracture specimens.

Mathematical characterization of maize canopies

Leaf area and its distribution in space largely determine canopy photosynthesis and dry matter accumulation. Methods were developed to characterize the morphology of maize plants in order to calculate leaf area and leaf angle distributions. Plants were placed against a grid where ligule heights and leaf curvature characteristics were measured. Leaf widths were then measured every 10 cm along the length of the leaf. The curvature of each leaf was characterized by a general quadratic equation expressed in terms of the initial leaf angle, the coordinates of the maximum height of the leaf and the coordinates of the leaf tip. A third order polynomial, expressed in terms of leaf width at the ligule, the length of the leaf and two empirical shape coefficients, was used to describe leaf shape. From these equations leaf areas were calculated as a function of plant height and distance between rows. Leaf angle distributions were also calculated. In order to reduce the number of coefficients needed to describe a canopy, the various parameters involved with leaf curvature and shape and internode length were fitted by least squares to second order polynomial functions of leaf number. These second order polynomial functions were used to generate leaf area and angle distributions which compared favourably with the original measurements.

Initiation, Propagation, and Kinking of an Antiplane Crack

An infinite linear elastic body containing a semi-infinite crack is loaded by a planar antiplane stress pulse parallel to the crack. The stress wave strikes the crack at time t=0 and at some arbitrary later time tf, the crack begins to extend straight ahead with constant speed vo. After some later tb, the crack suddenly stops, then kinks and propagates with constant speed vc, making an angle δ with the original crack. A superposition scheme is used to construct the exact full-field solution of the propagating crack. The full-field solution for stresses for the constant speed propagating crack with a delay time tf is found to be the Mode III analog of Baker’s problem in Mode I plus the stress pulse, and the displacement on the crack faces behind the moving crack tip is just the solution of Baker’s problem when expressed in crack tip coordinates and is independent of the delay time tf. When the crack suddenly stops, the stress field, which is radiated out from the stopped crack tip, corresponds to the stationary crack stress field of a crack whose crack tip has been at the stopped crack position for all time. The dynamic stress intensity factor at the kinked crack tip is then obtained by using a perturbation method. The region of the stress intensity factor controlled field is investigated for both stationary and propagating cracks. It is found that this region depends on the loading conditions and which stress components are considered. The region also depends on the crack tip speed and will contract as the crack tip speed increases.

Order-clustering of secant tips into edges for positioning of semiconductor structures

The paper presents the concept of order-clustering applied for recognition of edges and corners of polygonal objects, especially of two-dimensional shapes met in microelectronics. The recognition process starts with slicing an image into secants. The secant tips are clustered according to the scanning direction. Edge inclination is chosen as one of the main criteria of the order-clustering, enabling parallel shape analysis of each edge inclination (type) without losing the track of edge continuity. A specific distance criterion combined with the order-clustering eliminates arduous disturbances. The nearest neighbor order-clustering appends a tip of a secant to a cluster of edge type when the tip is the closest to the recent element of the edge type and when it satisfies an assumed order for the tip coordinates. The new secant tip is selected from the next line of an image. The superposition of the following factors: secant begginings, secant ends, nonascending order of secant tips and non-descending order of secant tips, allows clustering of edges into four basic types. An additional criterion of a minimum distance splits each edge type into two. The edges are clustered into continuous segments: if the candidate element does not satisfy all the assumed criteria, the recent element of the cluster is treated as the last element of a continuous edge segment. Two continuous segments belonging to different clusters of edges are merged into a corner if they are of sufficient lengths and if they are sufficiently close to each other. Polygons are clustered by merging corners of different types. An example of reconstruction of tetragons is presented.