Slice Of Thickness Research Articles

Research status of cardiac image segmentation based on deep learning

面对严重的医学影像分析缺口，深度学习的发展能够满足国内医疗行业的需求。心脏图像的处理方法可大致分为传统的图像处理技术、基于图谱的方法（atlas-based methods）、基于模型的方法（model-based methods）以及目前热门的采用机器学习和深度学习的方法。在深度学习兴起之前，传统的机器学习技术如模型法和图集法在心脏图像分割中有良好表现，但通常需要大量的特征工程知识或先验知识才能获得令人满意的精度。而基于深度学习的算法能从数据中自动发现复杂的特征以进行对象检测和分割。得益于先进的计算机硬件以及更多可用于训练的数据集，基于深度学习的分割算法已超越了以往的传统方法。本文回顾了2012—2022年有关心室、心外膜和心包脂肪的图像处理的各项方法、衡量指标及其目前的研究现状，并结合分割技术的发展，讨论了心脏分割的发展趋势。;Human-cardiovascular disease is challenged for its high morbidity and severe sequelae nowadays. To meet the need of the medical industry, current medical image analysis is facilitated via the development of deep learning. Conventional image processing technology is processed basically in terms of thresholding. The emerging deep learning technique can be focused on reality-oriented function in terms of specific eigenvalues. Such deep residual network and generative confrontation network have its potentials for its effectiveness and robust originated from good learning ability and data-driven factors. Our critical analysis is based on 1) characteristics of representative methods, 2) resources and scale of cardiac images, 3) comparative study of the performance evaluation and application conclusions of different methods through popular evaluation indicators, and 4) clinical domains are discussed as well. The literature review is originated from IEEE, SPIE, and China National Knowledge Network, with image processing and heart as search keywords. The difference between image processing methods is evaluated in terms of Dice coefficient and Hausdorff distance, and the performance is evaluated in quantitative further. For chamber segmentation, several approaches for right ventricle segmentation are reviewed and analyzed. As far as the principle of the segmentation method is concerned, the single of threshold is still challenged for segmentation unless it is integrated into other related methods, so it cannot be used as a single zone in segmentation technique. A brief theoretical introduction is mentioned for each method. Then, its methodology, prior datasets, and the effectiveness of segmentation process are involved in evaluation. Finally, the pros and cons of each method are analyzed as well. For the domain of epicardium and pericardium tissue, we will briefly introduce the popular image processing techniques for segmenting epicardium and pericardium tissue. Four category of key methods are analyzed in relevance to its:traditional image processing methods, atlas-based methods, machine learning, and deep learning. Traditional image processing methods are composed of such techniques of thresholding, region growing, and active contouring. Finally, Dice coefficient-derived capabilities of each algorithm are compared horizontally. For the segmentation method of the epicardium, it is easier to segment the epicardium into pericardium-illustrated coordination. Epicardial and pericardial fatty tissue are unevenly distributed around the heart, resulting in large sections-between variability and the images-between for its computed tomography (CT) and magnetic resonance imaging (MRI). The heterogeneity in shape is required to demonstrate further. However, the pericardium is featured of more smoother, thinner and oval in CT and MRI images. Such methods of active contours or ellipse fitting are suitable for segmenting such shapes naturally. Once the pericardium is divided, the epicardium is more easily divided into all pericardium-within fatty tissue. The great challenge is focused on epicardiumthinner segmentation. The slice of thickness can be set at 2~3 mm when CT scans are collected for coronary artery calcification (CAC) scoring. The pericardium is usually less than 2 mm thick, and it will often appear blurred or blurred on CT images in accordance with partial volume averaging, especially for heart organ-moving consistency. Some methods are purely pericardial delineation methods, while others are part of a method to segment and quantify the epicardium. For the epicardium part, we will mainly introduce the method of epicardium segmentation by the first pericardium-segmented. Pericardial fat segmentation methods typically rely on traditional image processing methods, such as 1) thresholding and region growing, and 2) various preprogrammed heuristics can be used to identify common structures and segment pericardial fat. Recent atlas-based segmentation approaches are employed but its clinical ability is relatively weakened. After current situation of segmentation is introduced, we will introduce some real scenarios applied in clinical practice. We can see that cardiac image processing has a large number of clinical problems are required to be solved. At the same time, we will briefly introduce the market situation of image processing in domestic market, integration of industry, education and research, and the main relevant policy trends. the development of the main related industries is introduced and involve in like 1) the establishment of related imaging databases in China, 2) the development of related imaging technologies in China, and 3) the development of related hardware equipment in China. At the end, it is discussed that the development of cardiac image segmentation processing is increasingly inseparable in related to the development of deep learning. However, because deep learning itself is difficult to be explained, we called on medical knowledge-interpreted method models, and deep learning based constraints are called to be resolved further, such homogeneity data sets and its related of higher accuracy.

Identification of fibrosis in hypertrophic cardiomyopathy: a radiomic study on cardiac magnetic resonance cine imaging

ObjectivesHypertrophic cardiomyopathy (HCM) often requires repeated enhanced cardiac magnetic resonance (CMR) imaging to detect fibrosis. We aimed to develop a practical model based on cine imaging to help identify patients with high risk of fibrosis and screen out patients without fibrosis to avoid unnecessary injection of contrast.MethodsA total of 273 patients with HCM were divided into training and test sets at a ratio of 7:3. Logistic regression analysis was used to find predictive image features to construct CMR model. Radiomic features were derived from the maximal wall thickness (MWT) slice and entire left ventricular (LV) myocardium. Extreme gradient boosting was used to build radiomic models. Integrated models were established by fusing image features and radiomic models. The model performance was validated in the test set and assessed by ROC and calibration curve and decision curve analysis (DCA).ResultsWe established five prediction models, including CMR, R1 (based on the MWT slice), R2 (based on the entire LV myocardium), and two integrated models (ICMR+R1 and ICMR+R2). In the test set, ICMR+R2 model had an excellent AUC value (0.898), diagnostic accuracy (89.02%), sensitivity (92.54%), and F1 score (93.23%) in identifying patients with positive late gadolinium enhancement. The calibration plots and DCA indicated that ICMR+R2 model was well-calibrated and presented a better net benefit than other models.ConclusionsA predictive model that fused image and radiomic features from the entire LV myocardium had good diagnostic performance, robustness, and clinical utility.Key Points• Hypertrophic cardiomyopathy is prone to fibrosis, requiring patients to undergo repeated enhanced cardiac magnetic resonance imaging to detect fibrosis over their lifetime follow-up.• A predictive model based on the entire left ventricular myocardium outperformed a model based on a slice of the maximal wall thickness.• A predictive model that fused image and radiomic features from the entire left ventricular myocardium had excellent diagnostic performance, robustness, and clinical utility.

Prevalence of incidental maxillary sinus pathology in asymptomatic patient during routine dental examination by Cone beam computed tomography(A Retrospective Study).

Abstract: Objective: The aim of the present study was to assess and to record the prevalence of incidental maxillary sinus pathologies in asymptomatic patients presenting with dental problems using the cone-beam computed tomography (CBCT) scans. Method: This retrospective study included 53 patients (106 maxillary sinus) underwent cone beam CT for various dental procedure, which included dental implants, maxillofacial surgery, orthodontics, endodontics, oral pathology, etc. Both male and female included in this study with age range from (18-45). Individuals with known sinus pathology were excluded in this study. The CBCT scans were evaluated and the maxillary sinuses ware examined by an experienced maxillofacial radiologist for the presence or absence of the any pathology. The images were analyzed in three planes (axial, sagittal and coronal) with a slice of (0.15 mm) thickness. Result: Among total of fifty-three cases included in the current study 35 (66.1%) of them had lesion with 47.2% they get their lesion on both sides followed by (13.2%,5.7%) on the left and right side respectively. while 18 individuals were free from any documented lesion. Regarding gender distribution in our study the females were predominant 54.7%. Conclusion: Oral radiologist should be aware of these incidental findings and thoroughly evaluate the whole captured CBCT volume in all 3 views (axial, coronal, and sagittal) to exclude any pathologic changes in the maxillary sinus, which can help in early diagnosis and refer the patient to a specialist if necessary for treatment. Keywords: Cone beam computed tomography, asymptomatic sinuses, pathology.

Evaluation of Sagittal Root Positions and Bone Perforation in Anterior Teeth Using Cone Beam Computed Tomography: An Observational Study.

Cone beam computed tomography (CBCT) and virtual implant help clinicians assess implant positioning with nearby vital structures and plan implant surgical procedures. Thus, the current study aims to evaluate the anterior sagittal root position and assess labial bone perforations in CBCT images. This study was carried out using CBCT scans of 140 samples involving 1338 teeth. The Digital Imaging and Communications in Medicine (DICOM) files were imported into Carestream 3-dimensional imaging software for analysis. All measurements were made in the appropriate section slice of 200-μm thickness in a darkened room. A standardized orientation was established by 2 examiners. The sagittal root positions (SRPs) were assessed in maxillary and mandibular anterior teeth. Labial bone perforation (LBP) was assessed using tapered implants in the virtual implant software. Overall, Class I SRP was highest (81.48% and 38.49%, respectively) in both the sextants. The SRP for Class I was most prevalent in canine teeth in both arches (87.96% and 56.45%, respectively), followed by incisors in other types in the maxillary arch. In the mandibular arch, both incisors were in Class IV and I relationships. The overall LBP was 4.26% and was more likely in the mandibular arch (5.64%) than in the maxillary arch (2.8%). The mandibular central incisors showed the highest rate of perforation (8.5% to 11.93%). The SRP and LBP did not show a statistically significant difference between the right and left sides in both arches. The correlation coefficient between SRP and LBP showed a statistically significant result (P < .01). Class I SRP was the most prevalent in maxillary and mandibular arches. Significantly more perforations occurred with mandibular anterior teeth and in Class IV SRP types (approximately 10% to 30%), which suggests that implant placement requires careful presurgical planning and regenerative approaches or delayed implant placement may be considered.

Effect of vertical seismic coefficient on cohesive-frictional soil slope under generalised seismic conditions

ABSTRACT In the present work, seismic performance parameters have been reviewed by considering the possible combined action of vertical and horizontal seismic loadings of the ground motion during the earthquakes. Analytical expressions of factor of safety, yield seismic coefficient and permanent seismic displacement of a cohesive-frictional soil slope have been developed by following deterministic sliding block approach in a two-dimensional pseudo-static framework. The slope with a planar failure surface is assumed to follow the Mohr-Coulomb criterion by considering a slice of unit thickness through the slope. For a given range of slope geometrical and soil parameters, the role of vertical seismic coefficient has been analysed in the presence of cohesion to investigate its effect on factor of safety, yield seismic coefficient, and consequently on the permanent seismic displacement of the slope through a set of graphical presentations. The results show that avoidance of vertical seismic component of the ground motion in the stability analysis may lead to severe slope failures. The general expressions proposed herein can be used to carry out a quantitative stability assessment of cohesive- frictional soil slopes during earthquakes in real-life projects.

TU‐A‐12A‐07: CT‐Based Biomarkers to Characterize Lung Lesion: Effects of CT Dose, Slice Thickness and Reconstruction Algorithm Based Upon a Phantom Study

Purpose:Radiogenomics promises the ability to study cancer tumor genotype from the phenotype obtained through radiographic imaging. However, little attention has been paid to the sensitivity of image features, the image‐based biomarkers, to imaging acquisition techniques. This study explores the impact of CT dose, slice thickness and reconstruction algorithm on measuring image features using a thorax phantom.Methods:Twentyfour phantom lesions of known volume (1 and 2mm), shape (spherical, elliptical, lobular and spicular) and density (‐630, ‐10 and +100 HU) were scanned on a GE VCT at four doses (25, 50, 100, and 200 mAs). For each scan, six image series were reconstructed at three slice thicknesses of 5, 2.5 and 1.25mm with continuous intervals, using the lung and standard reconstruction algorithms. The lesions were segmented with an in‐house 3D algorithm. Fifty (50) image features representing lesion size, shape, edge, and density distribution/texture were computed. Regression method was employed to analyze the effect of CT dose, slice of thickness and reconstruction algorithm on these features adjusting 3 confounding factors (size, density and shape of phantom lesions).Results:The coefficients of CT dose, slice thickness and reconstruction algorithm are presented in Table 1 in the supplementary material. No significant difference was found between the image features calculated on low dose CT scans (25mAs and 50mAs). About 50% texture features were found statistically different between low doses and high doses (100 and 200mAs). Significant differences were found for almost all features when calculated on 1.25mm, 2.5mm, and 5mm slice thickness images. Reconstruction algorithms significantly affected all density‐based image features, but not morphological features.Conclusions:There is a great need to standardize the CT imaging protocols for radiogenomics study because CT dose, slice thickness and reconstruction algorithm impact quantitative image features to various degrees as our study has shown.

Transport and magnetic properties of Fe/GaAs Schottky junctions for spin polarimetry applications

The electrical, magnetic and spin-filtering properties of Pd/Fe/GaAs(001) junctions are investigated. The Pd/Fe thin layers are deposited on GaAs(001) surfaces both clean and passivated by a thin oxide layer. The surface composition, structure and electronic properties of the starting surfaces are studied by means of XPS, LEED, EELS and photoreflectance. The Fe layer magnetic properties are characterized by magneto-optical Kerr effect (MOKE) measurements, while the electronic properties of the junctions are characterized by current-voltage (I-V) and photoreflectance measurements. For both types of substrate surfaces, the magnetization of the Fe layers is found close to that of a bulk Fe slice of equivalent thickness. For the oxide interface, the I-V curve exhibits almost an ideal Schottkylike behavior, since it can be very well interpreted by the thermoionic equation, using the ideality factor of n = 1.02 and surface barrier ϕb = 0.7 eV. For junctions prepared on the reconstructed GaAs(001) surface, the ideality factor and barrier heights are found in the range of 1.06–1.2 and 0.60–0.75 eV, respectively. Both structures give rise to similar spin filter effects under injection of spin-polarized electrons.

Effect of Surcharge on the Stability of Anchored Rock Slope with Water Filled Tension Crack under Seismic Loading Condition

In this paper, an analytical expression is derived for the factor of safety of the rock slope incorporating most of the practically occurring destabilizing forces as well as the external stabilizing force through an anchoring system. The slope stability is analyzed as a two-dimensional problem, considering a slice of unit thickness through the slope and assuming negligible resistance to sliding at the lateral boundaries of the sliding block. A detailed parametric study is presented to investigate the effect of surcharge on the stability of the rock slope for practical ranges of governing parameters such as inclination of the slope face, inclination of the failure plane, depth of tension crack, depth of water in tension crack, shear strength parameters of the material at the failure plane, unit weight of rock, stabilizing force and its inclination, and seismic load. For the range of parameters considered in the present study, it is found that the factor of safety of the rock slope decreases with increase in surcharge; the rate of decrease being relatively higher for lower values of surcharge. It is also observed that for a specific surcharge, the factor of safety depends significantly on all other parameters, except for unit weight of rock and higher values of inclination of stabilizing force to the normal at the failure plane. For any combination of these variables, the surcharge plays a vital role in the stability. A perfectly stable slope at relatively low surcharge can become unsafe with the increase in surcharge. The deterioration in the stability can be quite rapid, depending on the combination of the factors under consideration. The analysis and the general expression proposed herein can be used to carry out a quantitative assessment of the stability of the rock slopes.

Radiopacity of tantalum oxide nanoparticle filled resins

Objectives: Radiopacity of composite resins allows radiographic distinction of existing restorations and recurrent caries. Current composites must be supplemented with heavy metal-containing glasses or minerals to achieve a desired radiopacity. The purpose of this study was to evaluate the radiopacity of Tantalum oxide (Ta 2O 5) filled resins at varying percentage loadings. Methods: Methacrylate functionalized Ta 2O 5 nanoparticles (<50 nm) in methanol-dissolved or powder forms were mixed into either glycerol dimethacrylate (GDMA) or a bisGMA, TEGDMA, bisEMA mixture (GTE). Specimens were made in a split brass mold (2×2×15 mm) and compared with an aluminum stepwedge (99.5% pure Al) and a dentin slice of the same thickness. Kodak Ultraspeed periapical X-ray film on a lead plate at a target distance of 45 cm was exposed at 70 kVp and 10 mA, for 0.5 s and processed automatically. Optical density was measured ( n=3) with an RMI Processor Control Densitometer. Radiopacity was calculated as percent relative linear attenuation coefficient (Alpha). ANOVA and Student–Newman–Keuls comparisons were used to determine significance at the 95% confidence level. Results: Radiopacity increased significantly with Ta 2O 5 loading ( p=0.001). Ta 2O 5 nanoparticle filled resins enter the optimal range of diagnostic detectability ( α=150–250) at 50 wt.% and approach equivalence with enamel at approximately 70 wt.%. Significance: The introduction of tantalum oxide nanoparticle filler has potential as a miscible component of a resin composite to provide radiopacity for microfiller-type restorative materials and to circumvent the need for hydrolysis-prone glass reinforcing fillers.

Estimation of capillary length density in skeletal muscle by unbiased stereological methods: II. Use of vertical slices of unknown thickness.

The capillary network of the skeletal muscle was analyzed from a quantitative point of view with the purpose of determining the capillary length density--LV(cap/mus). A recent stereological method was applied to estimate this quantity using vertical slices of unknown thickness. First, the whole muscle was systematically sampled according to the fractionator method. The capillary length density was estimated on each chosen field of vision where the vertical axis was always identified as parallel to the major axis of the muscle fibers. Three measurements were performed: count of intersections between capillaries and cycloid test lines, count of intersections between capillaries and straight test lines, and count of capillary end points corresponding to the intersections of capillaries with the parallel planes of the vertical slices. The estimated capillary length density was 1,578 mm per mm3 of skeletal muscle tissue. The average thickness of the vertical slices was also estimated as 23.4 microns, which is roughly 6% less than the thickness measured using the microcator information on the microscope stage displacement. The advantages of this methodology were based on two main features: the method is assumption-free on the degree of capillary and muscle anisotropy, and the thickness of the vertical slices need not be known nor constant.

Regional aortic compliance studied by magnetic resonance imaging: the effects of age, training, and coronary artery disease.

Arterial compliance was measured in 70 healthy volunteers, 13 athletes, and 17 patients with coronary artery disease. Magnetic resonance images were acquired at end diastole and end systole through the ascending aorta, the aortic arch, and the descending thoracic aorta. Regional compliance was derived from the change in luminal area in a slice of known thickness and from the pulse pressure. Total arterial compliance was also measured from the left ventricular stroke volume and the pulse pressure. In the volunteers, mean (SD) regional compliance (microliters/mm Hg) was greatest in the ascending aorta (37 (18], lower in the arch (31 (15], and lowest in the descending aorta (18 (8], and it decreased with age. Compliance in the athletes was significantly higher than in their age matched controls (41 (16) versus 22 (11) microliters/mm Hg). In the patients with coronary artery disease it was significantly lower (12 (4) v 18 (10] than in age matched controls. Total arterial compliance also fell with age in those with coronary artery disease although there was more variation. The results suggest a possible role for compliance in the assessment of cardiovascular fitness and the detection of coronary artery disease.

Design of Neutron Detectors Utilising Luminescent Glass

The impetus for the development of new neutron detector designs has come from the worldwide commissioning of neutron spallation sources. The feature of these sources is their broadband neutron emission and the consequent potential which they provide for neutron investigation of all types of structures in materials ranging from biological molecules to steels. The primary advantage of conventional neutron detectors filled with boron fluoride or helium 3 gas is their intrinsically low background count; their major drawback is a slow response time, high cost, and relative inflexibility in design for coping with large areas or complex geometry detection. This paper presents design strategies for glass neutron scintillators. These lithium silicate glasses, doped with Cesium ions, have high detection efficiencies for neutrons, fast decay times, total flexibility in shape and emission centered at 400 nm, and can be well matched to PM and image intensifier photocathodes. The neutron counting applications require one or a combination of the following systems: for neutron flux counting, a slice of glass of appropriate thickness coupled to a PM/photodiode feeding an operational amplifier and scaler; with no appreciable x-ray or other interfering radiation present, a slice of glass oc appropriate thickness coupled to a PM, amore » Schmitt trigger, and a window discriminator; for low signal-to-noise ratio, a sandwich layer construction.« less

Thick section stereology for random fibres

The intersection of a random fibre process in Rn with an n-dimensional flat slice of thickness d is projected on a boundary hyperplane of the slice. The main result of the paper are stereological formulae for determining the mean fibre number and the mean fibre length of the process by the corresponding parameters of the projected fibre set provided the pr unary process is weaxLty mouion invariant)

A horizontal monolithic series-array solar battery employing thermomigration

By using the thermomigration process of Anthony and Cline (based upon Pfann’s temperature-gradient zone-melting process of the fifties) we have produced parallel aluminum-doped zones extending entirely through an n-type silicon slice of normal thickness. By applying a shallow p-type emitter diffusion to one face and interrupting it within each ’’cell’’ by means of an n+stripe that makes contact to the n-type base of the cell, we have realized a monolithic series-array solar battery, with results that constitute a feasibility demonstration of the method. Its advantages are permitting the entire thickness of the slice to constitute an active region and avoiding more costly dielectric isolation of cells or hand assembly of cells.

Ectomography : A New Radiographic Method for Reproducing a Selected Slice of Rarying Thickness

Ectomography : A New Radiographic Method for Reproducing a Selected Slice of Rarying Thickness

The attachment energy as a habit controlling factor: I. Theoretical considerations

The habit controlling factors in various crystal growth models (screw dislocation mechanism, two-dimensional nucleation, computer simulation models) are considered and related to the attachment energy E att, defined as the energy per molecule released when one slice of thickness d hkl crystallizes onto a crystal face ( hkl). It is found that the relative growth rate R of a face always increases with increasing E att, although the form of the function R( E att) depends on the growth mechanism and on various variables such as supersaturation, temperature and solid-fluid interaction. The crystal habit tends to be isometric in the case of the linear BCF law, while it obtains extreme forms when the quadratic BCF law or a polynucleation model applies. In the region of the quadratic BCF law the habit is independent on supersaturation, while in the linear BCF region or in the polynucleation region a higher supersaturation causes the habit to be more isometric. The fact that crystal habits often follow the geometrical law of Donnay and Harker can be understood from the relatively small orientation dependence of the specific surface energy.

Permeability of composite chondrocyte-culture-millipore membranes to solutes of varying size and shape.

A model connective-tissue system was developed that is amenable to the determination of permeability coefficients of diffusing solutes. The system involves the culture of 13-day chick-embryo chondrocytes on a Millipore filter (HA:0.45 micron pore size) to form what is, in effect, a confluent, extremely thin cartilage slice of uniform thickness. These cultured chondrocyte membranes were used to measure the steady-state flux of radioactively labelled low-molecular-weight solutes and micro-ions. Similarly, the permeability coefficients of either radioactively labelled or enzymically active proteins across the membranes were determined. The membrane was found to have no marked effects on the diffusional behaviour of low-molecular-weight non-electrolytes (water, proline, ribose, glucose, sorbitol, raffinose). For micro-ions (Na+, SO42-, Cl-, glutamate, glucuronate,), the diffusive behaviour was found to be markedly affected by the ionic strength of the solvent used in a manner which was consistent with a Donnan distribution resulting from the immobilized proteoglycans. Globular proteins permeated the membrane at rates which decreased as the molecular size of the diffusing solute increased. The apparent diffusion rates of fibrinogen and of collagen through the membranes were greater than would be expected on the basis of their diffusion coefficients in free solution. Reasons for this behaviour are discussed.

Estimating aggregate and overall characteristics from thick sections by transmission microscopy

SUMMARYThe random spatial structure considered is the union X of an aggregate of random opaque convex particles in transparent space, the particle centroids being sited at the points of a homogeneous Poisson process. The model is thus the union of an aggregate of non‐necessarily‐convex disjoint regions. Expressions are derived for the fundamental stereological quantities VV, SV, KV (integrated mean curvature density) and GV (integrated gaussian curvature density) for X; and for AA, LA and CA (integrated curvature density) for the projection of a slice of thickness t of this model onto a plane parallel to the slice, where t may take any non‐negative value. The estimates relevant to transmission microscopy suggested by this theory are presented.

One-Dimensional Equations of Open-Channel Flow

One-dimensional equations of continuity, momentum, and energy for unsteady, spatially varied flow in a fixed-bed open channel of arbitrary configuration are derived from the point forms of the corresponding hydrodynamic equations by integrating the latter over a deforming region of space comprising a slice of differential thickness across the flow with a top always coincident with the fluctuating water surface. To bring the equations to the form of Saint Venant in fixed and accelerating reference frames, departures from hydrostatic pressure conditions in a cross section due to lateral acceleration, viscous deformation, and turbulent Reynolds stresses are reproduced exactly; the rate of energy dissipation in a cross section is uniquely related to wall shear over the wetted perimeter; the term accounting for lateral discharge depends upon its nature; bulk outflow is considered.

On Edge Dislocations in a Possible Relation to Structure of a Crystal Surface

Stresses around an edge dislocation near a free surface are calculated using two kinds of elastic representations (Volterra dislocations): One is a ring deformed by removal of a slice of uniform thickness and the other is a ring deformed by slip. Only the former is shown to yield a stable network plane of dislocations parallel to a free surface. The conditions of stability of the network plane are discussed in relation to a compressive surface stress. The network plane seems to give a possible explanation of superstructures observed on the (111) surfaces of diamond-type crystals.