Gaussian Curvature Analysis Research Articles

Accurate tissue flap reconstruction method based on the quadratic surface developability for head and neck soft tissue defects

Soft tissue defects resulting from head and neck tumor resection seriously impact the physical appearance and psychological well-being of patients. The complex curvature of the human head and neck poses a formidable challenge for maxillofacial surgeons to achieve precise aesthetic and functional restoration after surgery. To this end, a normal head and neck volunteer was selected as the subject of investigation. Employing Gaussian curvature analysis, combined with mechanical constraints and principal curvature analysis methods of soft tissue clinical treatment, a precise developable/non-developable area partition map of the head and neck surface was obtained, and a non-developable surface was constructed. Subsequently, a digital design method was proposed for the repair of head and neck soft tissue defects, and an in vitro simulated surgery experiment was conducted. Clinical verification was performed on a patient with tonsil tumor, and the results demonstrated that digital technology-designed flaps improved the accuracy and aesthetic outcome of head and neck soft tissue defect repair surgery. This study validates the feasibility of digital precision repair technology for soft tissue defects after head and neck tumor resection, which effectively assists surgeons in achieving precise flap transplantation reconstruction and improves patients' postoperative satisfaction.

Ball Pivoting Algorithm and discrete gaussian curvature: A direct way to curved nanographene circularly polarized luminescence spectral simulation

Theoretical innovations for constructing robust computational protocols are of fundamental significance for a variety of advanced chiroptical spectroscopies. The new generation of chiral curved nanographenes offered us the opportunity to study the chiral emission phenomena in the nanometers scale. Herein we reported a distinctive method that combines topological aspects and the density functional theory in order to reach a coherent description of calculated circularly polarized luminescence spectra of negatively curved nanographenes. Our computational plan was defined as a multi-sequence strategy, paying the attention on the relationship between the molecular curvature and the relative spectroscopic properties: 1) the Ball Pivoting Algorithm for the nanographene surface reconstruction; 2) the atom by atom discrete gaussian curvature analysis to establish which DFT functional better approximates the shape of nanographenes backbones; 3) molecular dynamics in the first excited state for accounting the thermal effect; 4) TDDFT benchmark to scrutinize which functional provides the most reliable excitation energies and rotatory strengths for an accurate CPL spectral simulation. The direct merging of the previous steps celebrated the B3LYP (coupled with the 6-311G(d,p) basis set) as the most precise exchange–correlation functional in duplicating exquisitely the CPL profiles of a heterogeneous set of functionalized nanographene.

Vibrationally resolved deep–red circularly polarised luminescence spectra of C70 derivative through Gaussian curvature analysis of ground and excited states

Over the last years, the interaction of fullerene with circularly polarized light has attracted growing attention for potential electronic and optical applications. However, in literature there is only one example of fullerene derivative capable of emitting circularly polarized light, showing an active circularly polarized luminescence (CPL) signal in the deep-red visible region. This unique luminophore offered us the possibility to study the connection between the topological features of C70 spheroid and its chiral emission properties. In light of these considerations, we proposed a theoretical protocol that combines three different step: (1) The Ball Pivoting Algorithm for C70 surface reconstruction. (2) The discrete gaussian curvature analysis in the ground (S0) and excited states (S1). (3) The computation of the vibrationally-resolved CPL spectrum. The first step allowed us to extract useful information that linked the topological shape of C70 to the sp2 carbon network chemistry. The DFT benchmark in the second step guided us in grasping the best functional for the C70 curvature simulation in the ground state, spotlighting how B97D3 excellently succeed for this task. The curvature investigation in the first excited state showed that (for all the twenty exchange–correlation functional tested) the C70 fragment is more curved in S1 than in S0. The final step collected the topological information from the previous sections to provide a detailed overview of the theoretical factors (such as the quantum formalism, the potential energy surface description and the transition dipole moment approximation) impacting on the C70 vibrationally resolved CPL spectrum. We found that the adiabatic hessian model coupled with the Franck-Condon Herzberg-Teller approximation computed at PW6B95D3/6-311G(d,p) level provides excellent results in emulating the band-shape and position of the experimental CPL spectrum.

A Region-Based Statistical Shape Modeling on the First Trapezoid-Metacarpal.

A statistical shape model (SSM) based analysis was conducted in our study. We indicated the morphological differences of the first trapezoid-metacarpal (TMC) bone between the region-based statistical shape model (rSSM) and the nonregion-based statistical shape model (nrSSM). We aimed to characterize more specific and accurate variation results to detect and prevent osteoarthritis in an early way. CT image data of TMC from 31 healthy volunteers were simulated with 3D models. A training set of models was analyzed with principal component analysis, with both then- rSSM and rSSM. The region was identified automatically with Gaussian curvature analysis. We found four dominant shape variations from both nrSSM and rSSM. The rSSM showed more variations with fewer components compared with nrSSM. The first principal component revealed the size variation as the biggest component. A significant difference was presented in the second and the fourth principal component from rSSM, showing the torsion of the distal head of the first metacarpal which may increase the risk of osteoarthritis.

Near-miscible supercritical [formula omitted] injection in oil-wet carbonate: A pore-scale experimental investigation of wettability state and three-phase flow behavior

Near-miscible supercritical CO2 (scCO2) injection and its underlying pore-scale physics were experimentally investigated in an oil-wet carbonate rock at elevated temperature and pressure conditions using X-ray microtomography. The results of in situ contact angle measurements yielded direct evidence showing that the scCO2 injection triggered a wettability reversal process resulting in reduced oil-wetness. As the scCO2 injection progressed, we observed a distinct wettability state where the wetting preference of the solid to the scCO2, oil, and brine phases was similar due to the wettability reversal. Consequently, pore sizes neither dictated any preferential invasion order nor restricted the displacement efficiency of the injection process. Furthermore, we identified a type of spreading system where spreading oil layers formed but did not exist globally across the pore space between the scCO2 and brine phases. Gaussian curvature analysis showed that the scCO2 and oil phases were well-connected at the early stage of the scCO2 injection, whereas brine connectivity was relatively poor. As the injection continued, brine connectivity was improved due to the wettability reversal effect. Moreover, displacement events including double and multiple displacements were identified and discussed. They included a variety of events that had scCO2 as the first phase and oil and brine as the subsequent phases. The diversity and affordability of such displacements were much higher than those previously observed during N2 injection in oil-wet systems where mostly gas-to-oil-to-brine double displacements took place. The interplay of scCO2-oil miscibility, the distinctive wettability state, favorable fluid connectivity, and frequent double/multiple displacements resulted in an exceptional displacement efficiency during near-miscible scCO2 injection.

CT quantification of the heterogeneity of fibrosis boundaries in idiopathic pulmonary fibrosis.

ObjectivesTo quantify the heterogeneity of fibrosis boundaries in idiopathic pulmonary fibrosis (IPF) using the Gaussian curvature analysis for evaluating disease severity and predicting survival.MethodsWe retrospectively included 104 IPF patients and 52 controls who underwent baseline chest CT scans. Normal lungs below − 500 HU were segmented, and the boundary was three-dimensionally reconstructed using in-house software. Gaussian curvature analysis provided histogram features on the heterogeneity of the fibrosis boundary. We analyzed the correlations between histogram features and the gender-age-physiology (GAP) and CT fibrosis scores. We built a regression model to predict diffusing capacity of carbon monoxide (DLCO) using the histogram features and calculated the modified GAP (mGAP) score by replacing DLCO with the predicted DLCO. The performances of the GAP, CT-GAP, and mGAP scores were compared using 100 repeated random-split sets.ResultsPatients with moderate-to-severe IPF had more numerous Gaussian curvatures at the fibrosis boundary, lower uniformity, and lower 10th to 30th percentiles of Gaussian curvature than controls or patients with mild IPF (all p < 0.0033). The 20th percentile was most significantly correlated with the GAP score (r = − 0.357; p < 0.001) and the CT fibrosis score (r = − 0.343; p = 0.001). More numerous Gaussian curvatures, higher entropy, lower uniformity, and 10th to 30th percentiles (p < 0.001–0.041) were associated with mortality. The mGAP score was comparable to the GAP and CT-GAP scores for survival prediction (mean C-indices, 0.76 vs. 0.79 vs. 0.77, respectively).ConclusionsGaussian curvatures of fibrosis boundaries became more heterogeneous as the disease progressed, and heterogeneity was negatively associated with survival in IPF.Key Points • Gaussian curvature of the fibrotic lung boundary was more heterogeneous in patients with moderate-to-severe IPF than those with mild IPF or normal controls. • The 20th percentile of the Gaussian curvature of the fibrosis boundary was linearly correlated with the GAP score and the CT fibrosis score. • A modified GAP score that replaced the diffusing capacity of carbon monoxide with a composite measure using histogram features of the Gaussian curvature of the fibrosis boundary showed a comparable ability to predict survival to both the GAP and the CT-GAP score. Supplementary InformationThe online version contains supplementary material available at 10.1007/s00330-020-07594-y.

Gaussian Surface Curvature Mapping Indicating High Risk Type B Thoracic Aortic Dissections

Identifying fragile aortas that are more likely to lead to adverse clinical outcomes would provide surgeons with a better sense of how to balance the risks of surgical versus medical management in patients with type B dissections. We examine the progression of a type B dissection into a type A dissection in a patient and analyze changes in the Gaussian surface curvature distribution, as well as the response of the stress distribution at the lesser curve in response to pressurization. We hypothesize that examining the Gaussian curvature will provide us with a link between aortic surface geometry and the stress distribution, which is crucial to understanding the process driving aortic dissection. Computed tomography scans of a patient before and after the type A dissection are obtained. These are segmented in Simpleware ScanIP. Centerline curvatures are calculated on segmented models in ScanIP. Models are then pressurized in the finite element analysis software Abaqus. The Gaussian curvature is calculated by exporting segmentations into the computational program Matlab and applying a modified previously published algorithm. The centerlines generated in ScanIP fail to capture the change in the acuity of the lesser curve before and after the type A dissection. Instead, Gaussian curvature analysis shows that the curvature distribution before the type A dissection is much wider compared with the distribution after the type A dissection. In addition, analyzing the stress distribution in response to pressurization reveals that before the type A dissection there is a large divergence in the principal stress vectors at the lesser curve but this transitions to a more uniform hoop stress after the type A dissection. Our analysis demonstrates that Gaussian surface curvature analysis captures changes in aortic geometry that are otherwise silent in centerline curvature analysis. Here, we show that as the aorta develops a type A dissection it is able to more smoothly handle the hoop stress at the lesser curve compared with the stress focusing seen in the before type A geometry. We propose that the geometric focusing before type A creates a higher energy stress state, which is relaxed on retrograde dissection. Thus, Gaussian curvature analysis may provide a window to capture underlying geometric instability in type B dissections.

A reliable method for morphological measurement of 3D calcaneus models from computed tomography images.

The way to assess the calcaneal fractures reduction is still open. Anatomical morphology is an important clinical value to maintain normal function and may use as references to evaluate the reduction for calcaneal fractures. The aim of study is to provide reliable and repeatable three-dimensional (3D) morphology measurement. 3D models of ninety-nine Taiwanese normal calcaneus were reconstructed and segmented from CT image. Anatomical landmark serves as measurement constraints that manually identified and localized on bone mesh surface according to Gaussian curvature analysis. Computer assisted measurement and manual measurement were performed to quantify morphological parameters. Statistically, measurement results of calcaneal morphology were analyzed. The correlation between each of morphological parameters was tested using Bivariate-Pearson correlation. Gender differences relate to parameters were also tested. Intraclass correlation coefficient (ICC) and root mean square standard deviation (RMS-SD) were performed for reliable and precision study. Significant parameter differences between males and females were found (p 0.754). RMS-SD of precision for linear and angular measurement was adequate, around 0.8 mm and 1.7°. Morphological parameters for both male and female groups, 78.5 mm in length, 42.1 in height, 43.3 mm in width, 112.5° in Gissane angle, 33.4° in Bohler angle, which is not much different compared to Asian morphology population. The proposed method positively contributes to measurement calcaneal morphology with significant reliability and repeatability. This study may offer to be a basic data and reference for assessment calcaneal fracture reduction.

Constraints of deep crustal structures on large deposits in the Cloncurry district, Australia: Evidence from spatial analysis

Deep structures are commonly recognized as critical factors for controlling the formation of large hydrothermal deposits. It is of great importance for the metallogenic studies to quantitatively describe the spatial associations of deep structures with mineral deposits. In the Cloncurry district of the Mt. Isa Province, Australia, many large deposits have been discovered and district-scale deep structures have also been recognized from the magnetic, gravity, seismic and magnetotelluric data. In this paper, we delineate the 3D configuration of the deep structures by 3D geometric modeling and Gaussian curvature analysis, and quantify spatial associations of the deep structures with the large deposits by the weights of evidence method. The results demonstrate that the configuration of deep structures has a positive spatial constraint on the distribution of deposits. Many deposits are located close to the high curvature portion of the deep structures. According to this rule, there are some potential target areas where curvature of the deep structural surfaces is high but no deposits have been discovered. Such results can be used to identify targets with potential for finding undiscovered deposits.

Human eyeball model reconstruction and quantitative analysis.

Determining shape of the eyeball is important to diagnose eyeball disease like myopia. In this paper, we present an automatic approach to precisely reconstruct three dimensional geometric shape of eyeball from MR Images. The model development pipeline involved image segmentation, registration, B-Spline surface fitting and subdivision surface fitting, neither of which required manual interaction. From the high resolution resultant models, geometric characteristics of the eyeball can be accurately quantified and analyzed. In addition to the eight metrics commonly used by existing studies, we proposed two novel metrics, Gaussian Curvature Analysis and Sphere Distance Deviation, to quantify the cornea shape and the whole eyeball surface respectively. The experiment results showed that the reconstructed eyeball models accurately represent the complex morphology of the eye. The ten metrics parameterize the eyeball among different subjects, which can potentially be used for eye disease diagnosis.

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.

Surface size, curvature analysis, and assessment of knee joint incongruity with MRI in vivo.

The purpose of this study was to develop an MR-based technique for quantitative analysis of joint surface size, surface curvature, and joint incongruity and to assess its reproducibility under in vivo imaging conditions. The surface areas were determined after 3D reconstruction of the joint by triangulation and the incongruity by Gaussian curvature analysis. The precision was tested by analyzing four replicated MRI datasets of human knees in 14 individuals. The algorithms were shown to produce accurate data in geometric test objects. The interscan precision was <4% (CV%) for surface area, 2.9-5.7 m(-1) (SD) for the mean principal curvature, and 4.1-7.4 m(-1) for congruence indices. Incongruity was highest in the femoropatellar joint (79.7 m(-1)) and lowest in the medial femorotibial joint (28.6 m(-1)). This technique will permit identification of the specific role of surface size, curvature, and incongruity as potential risk factors for osteoarthritis.

Detection of zones of abnormal strains in structures using Gaussian curvature analysis : R. J. Lisle, American Association of Petroleum Geologists Bulletin, 78(12), 1994, pp 1811–1819

Detection of zones of abnormal strains in structures using Gaussian curvature analysis : R. J. Lisle, American Association of Petroleum Geologists Bulletin, 78(12), 1994, pp 1811–1819

Detection of Zones of Abnormal Strains in Structures Using Gaussian Curvature Analysis

Whereas some folds, such as those produced by flexural slip, do not theoretically entail strain within the folded surfaces, any surface involving double curvature (such as domes and saddles) cannot form without some stretching or contraction of the bedding. Whether straining of the surfaces is required during folding depends on the three-dimensional fold shape and, in particular, on the Gaussian curvature at points on the folded surface. Using this as a basis, I present a method for detecting zones of anomalously high strain in oil-field structures from Gaussian curvature analysis (GCA) of natural structures. The new method of GCA is suitable for analyzing surfaces that have been mapped seismically. A Gaussian curvature map of the structure is a principal outcome of the a alysis and can be used to predict the density of strain-related subseismic structures, such as small-scale fracturing. The Goose Egg dome, near Casper, Wyoming, is analyzed and provides an example of GCA. In this structure, a relationship is observed between fracture densities and Gaussian curvature.