Tortuosity Estimation Research Articles

Tortuosity of pore channels in tight rocks as a key parameter in fluid flow ability

Tortuosity is a significant parameter in porous materials analysis. Not only, when it comes to rocks or soils but also cellular materials, alloys or cells, the multiple definitions exist for tortuosity and several purposes. Geometrical tortuosity describes the pore network paths; on the other hand thermal, diffusional, electrical and hydraulic tortuosity refers to the transport processes in the pore network. Computed X-ray tomography (CT) is the best solution in tortuosity estimation, thanks to the 3D images. In particular, computed X-ray tomography, together with mercury porosimetry (MICP), pulse- and pressure-decay permeability methods (PDP), as well as electrical parameter measurements (EPM), links and expands the information about the tortuosity into the greater meaning. The geological material was composed of tight, low-porosity and low-permeability gas-saturated rocks cored from the present depth of deposition below 3000 m, containing different lithologies, as sandstones, mudstones, limestones, and dolomites. The research presents the novel approach in the identification and analysis of the main pore channels based on 3D CT images. Algorithm of the central axis identifies and analyzes the whole main flow path and calculates tortuosity. High correlation was observed between the tortuosity and Swanson parameter from mercury porosimetry data. Moreover, the high correlation was detected between the tortuosity and saturation exponent from electrical parameter measurement in analyzed tight low-porosity and low-permeability deposits. Multilinear regression (MLR) allows estimating absolute permeability taking CT, MICP and EPM parameters into consideration. Combination of these parameters in one equation with high determination coefficient gives credence in estimating preliminary absolute permeability (PDP) based on the data which is executed as standard core analysis (MICP and EPM) and data from the non-invasive method (CT).

Estimation of the aerodynamic tortuosity of woven/wire screens

The use of wire/woven screens (WSs) is frequent in applications such as particle or insect-proof screen in home/greenhouse/farm with natural ventilation. Although this passive element has been studied for decades, most previous works have focused on relating the airflow performance only to porosity. However, most recent investigations have demonstrated that other pore-related parameters such as constriction factor and tortuosity are necessary for the characterisation of screens. Tortuosity of WSs is a parameter that has been broadly estimated in the literature, whose calculations to date are not physics-based and yield a constant value without dependence on airflow velocity. The present investigation proposes a novel method to calculate tortuosity of WS. The new approach uses the flow potential flow theory to estimate realistic curvatures of the streamlines around the inclined threads of the WS. The calculated tortuosity has been made also velocity-dependent, because its value changes for Reynolds numbers below 200, generally. The accurate estimation of tortuosity is a very important contribution to the field, because it is a missing link to develop a universal model to estimate pressure drop for any WS performance. This calculation has been added to AeroScreen software, which allows to obtain porosity, constriction and tortuosity from geometry data.

Clinically Based Automated Tracing and Tortuosity Estimation of Corneal Nerve Fibers From Confocal Microscopy Images

The purpose of this study was the development of an algorithm able to automatically trace corneal nerves and to estimate a nerve tortuosity index that is useful in clinical practice. In vivo confocal microscopy is an imaging technique that allows the clinical assessment of corneal and systemic diseases. Many studies have demonstrated a correlation between the tortuosity level of nerve fibers in the subbasal plexus layer and some pathologies. We developed an algorithm that provides fully automatic tracing of nerve fibers. It also includes a new way of dealing with bifurcations, separating the main paths from the secondary ones. Based on this automated tracing, the tortuosity was estimated as the absolute curvature, tortuosity density, and fractal dimension. These metrics were considered first individually and then as a linear combination of 2 or 3 of them. We investigated the capability of the estimated tortuosity to emulate the clinical classification into low, mid, and high tortuosity levels. Furthermore, we investigated its ability to distinguish healthy subjects from pathological subjects. Excellent agreement between manual and automated grouping of tortuosity (96.6% accuracy) was obtained. Moreover, the proposed algorithm could differentiate between healthy and pathological subjects with an accuracy of 77.1% by analyzing each image individually. The accuracy improved to 86.31% by considering 3 images of the same subject simultaneously. The proposed framework provides completely automated analysis of corneal nerve images. The results demonstrate the ability of our method to emulate the clinical classification of tortuosity levels and its potential for identifying healthy and pathological subjects.

Electrical, Diffusional, Hydraulic, and Geometrical Tortuosity Anisotropy Quantification Using 3D Computed Tomography Scan Image Data

Summary Sedimentary rocks display complex spatial distribution of both pore space and solid components, impacting the directional dependence of physical phenomena such as electrical conduction, fluid flow, heat transfer, and molecular diffusion. The complexity of the pore space is often quantified by the concept of tortuosity, which measures the sinuosity of the connecting paths in the pore space. Tortuosity is an important quantity in formation evaluation as it impacts petrophysical properties such as permeability and formation factor. However, the existence of various techniques can lead to nonuniqueness in assessment of tortuosity. Furthermore, spatial variation of the solid components of the rocks occurring at the core-scale domain reflected in the connectivity and distribution of the minerals is typically not quantified. The objectives of this paper are (a) to quantify tortuosity and tortuosity anisotropy of porous media through estimation of electrical, diffusional, hydraulic, and geometrical tortuosity at the pore scale and core scale and (b) to compare electrical, diffusional, hydraulic, and geometrical tortuosity. We estimate tortuosity in the pore space of microcomputed tomography (micro-CT) scan images and in the most connected and abundant solid phase of whole-core CT scan images. We conduct numerical simulations of electric potential distribution, diffusion, and fluid flow and velocity distribution to estimate electrical, diffusional, and hydraulic tortuosity, respectively. To calculate geometrical tortuosity, we use the segmented pore space from micro-CT scan images to extract a pore network model and compute the shortest path of all opposing pores of the samples. Finally, tortuosity values obtained with each technique are used to assess the anisotropy of the samples. We applied the documented workflow to core- and pore-scale images. The CT scan images in the core-scale domain belong to a siliciclastic formation. Micro-CT scan images in the pore-scale domain were obtained from Berea Sandstone, Austin Chalk, and Estaillades limestone formations. We observed differences in estimates of direction-dependent electrical, diffusional, hydraulic, and geometrical tortuosity for both types of images. The highest numerical differences were observed when comparing streamline electrical and hydraulic tortuosity with diffusional tortuosity. The observed differences were significant in anisotropic samples. Differences in tortuosity estimates can impact the outcomes of rock physics models for which tortuosity is an input. The documented comparison provides insight in the selection of techniques for tortuosity estimation. Use of core-scale image data provides semicontinuous estimates of tortuosity and tortuosity anisotropy, which are typically not attainable using pore-scale images. Additionally, the semicontinuous tortuosity anisotropy estimates from whole-core CT scan images provide a tool for selection of best locations to take core plugs.

DeepGrading: Deep Learning Grading of Corneal Nerve Tortuosity.

Accurate estimation and quantification of the corneal nerve fiber tortuosity in corneal confocal microscopy (CCM) is of great importance for disease understanding and clinical decision-making. However, the grading of corneal nerve tortuosity remains a great challenge due to the lack of agreements on the definition and quantification of tortuosity. In this paper, we propose a fully automated deep learning method that performs image-level tortuosity grading of corneal nerves, which is based on CCM images and segmented corneal nerves to further improve the grading accuracy with interpretability principles. The proposed method consists of two stages: 1) A pre-trained feature extraction backbone over ImageNet is fine-tuned with a proposed novel bilinear attention (BA) module for the prediction of the regions of interest (ROIs) and coarse grading of the image. The BA module enhances the ability of the network to model long-range dependencies and global contexts of nerve fibers by capturing second-order statistics of high-level features. 2) An auxiliary tortuosity grading network (AuxNet) is proposed to obtain an auxiliary grading over the identified ROIs, enabling the coarse and additional gradings to be finally fused together for more accurate final results. The experimental results show that our method surpasses existing methods in tortuosity grading, and achieves an overall accuracy of 85.64% in four-level classification. We also validate it over a clinical dataset, and the statistical analysis demonstrates a significant difference of tortuosity levels between healthy control and diabetes group. We have released a dataset with 1500 CCM images and their manual annotations of four tortuosity levels for public access. The code is available at: https://github.com/iMED-Lab/TortuosityGrading.

An analysis of the influence of transfer learning when measuring the tortuosity of blood vessels

Background and Objective: Convolutional Neural Networks (CNNs) can provide excellent results regarding the segmentation of blood vessels. One important aspect of CNNs is that they can be trained on large amounts of data and then be made available, for instance, in image processing software. The pre-trained CNNs can then be easily applied in downstream blood vessel characterization tasks, such as the calculation of the length, tortuosity, or caliber of the blood vessels. Yet, it is still unclear if pre-trained CNNs can provide robust, unbiased, results in downstream tasks involving the morphological analysis of blood vessels. Here, we focus on measuring the tortuosity of blood vessels and investigate to which extent CNNs may provide biased tortuosity values even after fine-tuning the network to a new dataset under study. Methods: We develop a procedure for quantifying the influence of CNN pre-training in downstream analyses involving the measurement of morphological properties of blood vessels. Using the methodology, we compare the performance of CNNs that were trained on images containing blood vessels having high tortuosity with CNNs that were trained on blood vessels with low tortuosity and fine-tuned on blood vessels with high tortuosity. The opposite situation is also investigated.Results: We show that the tortuosity values obtained by a CNN trained from scratch on a dataset may not agree with those obtained by a fine-tuned network that was pre-trained on a dataset having different tortuosity statistics. In addition, we show that improving the segmentation accuracy does not necessarily lead to better tortuosity estimation. To mitigate the aforementioned issues, we propose the application of data augmentation techniques even in situations where they do not improve segmentation performance. For instance, we found that the application of elastic transformations was enough to prevent an underestimation of 8% of blood vessel tortuosity when applying CNNs to different datasets.Conclusions: The results highlight the importance of developing new methodologies for training CNNs with the specific goal of reducing the error of morphological measurements, as opposed to the traditional approach of using segmentation accuracy as a proxy metric for performance evaluation.

Automatic Tortuosity Estimation of Nerve Fibers and Retinal Vessels in Ophthalmic Images

The tortuosity changes of curvilinear anatomical organs such as nerve fibers or vessels have a close relationship with a number of diseases. Therefore, the automatic estimation and representation of the tortuosity is desired in medical image for such organs. In this paper, an automated framework for tortuosity estimation is proposed for corneal nerve and retinal vessel images. First, the weighted local phase tensor-based enhancement method is employed and the curvilinear structure is extracted from raw image. For each curvilinear structure with a different position and orientation, the curvature is measured by the exponential curvature estimation in the 3D space. Then, the tortuosity of an image is calculated as the weighted average of all the curvilinear structures. Our proposed framework has been evaluated on two corneal nerve fiber datasets and one retinal vessel dataset. Experiments on three curvilinear organ datasets demonstrate that our proposed tortuosity estimation method achieves a promising performance compared with other state-of-the-art methods in terms of accuracy and generality. In our nerve fiber dataset, the method achieved overall accuray of 0.820, and 0.734, 0.881 for sensitivity and specificity, respectively. The proposed method also achieved Spearman correlation scores 0.945 and 0.868 correlated with tortuosity grading ground truth for arteries and veins in the retinal vessel dataset. Furthermore, the manual labeled 403 corneal nerve fiber images with different levels of tortuosity, and all of them are also released for public access for further research.

A novel model for reservoir rock tortuosity estimation

This work presents a simple and novel model for determining the tortuosity of a porous, permeable rock – the ratio of a streamline path-length between two points to the straight-line distance between those points – a parameter which enables an estimate of permeability. Previous research on this topic has resulted in elaborate or complex models, partly due to confusion in terminology between tortuosity and tortuosity factor, and partly due to the difficulty in estimating the streamline path-length along which fluids flow. Tortuosity is a useful parameter that must be estimated from precise laboratory measurements of fluid flow through rock samples but from which the resulting empirical relationship is relatively arbitrary. This paper uses a poro geometry elasticity approach to create an innovative formulation and to determine the parameters in the model from precise experimental measurements. The underlying assumption in the formalism is that the inverse of the tortuosity factor is directly proportional to that of the porosity. The variation of tortuosity with respect to porosity results in an equation relating surface area strain with varying porosity values, and the reservoir tortuosity was conducted. The analysis shows an inverse relationship between tortuosity and porosity, as observed in the experimental data. I find that pore-thsurface arearoat occlusion significantly impacts pore connectivity for tight reservoir and reduces the prediction accuracy of tortuosity. I therefore conclude that the tortuosity model from this study is applicable to different reservoirs.

Automated Tortuosity Analysis of Nerve Fibers in Corneal Confocal Microscopy.

Precise characterization and analysis of corneal nerve fiber tortuosity are of great importance in facilitating examination and diagnosis of many eye-related diseases. In this paper we propose a fully automated method for image-level tortuosity estimation, comprising image enhancement, exponential curvature estimation, and tortuosity level classification. The image enhancement component is based on an extended Retinex model, which not only corrects imbalanced illumination and improves image contrast in an image, but also models noise explicitly to aid removal of imaging noise. Afterwards, we take advantage of exponential curvature estimation in the 3D space of positions and orientations to directly measure curvature based on the enhanced images, rather than relying on the explicit segmentation and skeletonization steps in a conventional pipeline usually with accumulated pre-processing errors. The proposed method has been applied over two corneal nerve microscopy datasets for the estimation of a tortuosity level for each image. The experimental results show that it performs better than several selected state-of-the-art methods. Furthermore, we have performed manual gradings at tortuosity level of four hundred and three corneal nerve microscopic images, and this dataset has been released for public access to facilitate other researchers in the community in carrying out further research on the same and related topics.

Novel technique to measure mutual bulk fluid diffusion using NMR 1-D gradient

Many modelling and theoretical studies have shown that diffusion can be a significant transport mechanism in low-permeability porous media. Understanding the process allows engineers to better predict reservoir performance during both primary production and enhanced recovery in unconventional reservoirs. Direct measurement of effective diffusion in tight rocks is difficult, due to small pore volumes and the lack of techniques to actually monitor the process. Conventional diffusion measurements generally require fluid sampling, which induces a pressure transient which changes the mass transfer mechanism. Previously, we introduced a novel technique to measure tortuosity in nano-porous media by simultaneously monitoring methane versus nitrogen concentrations at high pressure using transmission Infrared Spectroscopy (IR). To complete the estimation of effective diffusion, bulk fluid diffusion coefficient also needs to be measured. In this study, we demonstrate the usage of Nuclear Magnetic Resonance (NMR) 1-D imaging to examine the dynamic change of Hydrogen Index (HI) across the interface between two bulk fluids. The experiment was conducted between a crude oil sample and methane; fluid samples were pressurized within an NMR transparent ZrO2 pressure cell which operates at pressures up to 10,000 psi. The Hydrogen Index (HI) profile was continuously measured and recorded for 7 days. The results provided oil the swelling factor and the concentration profile as a function of both time and distance. These data then were fitted with Maxwell-Stefan equation to precisely back calculate the diffusion coefficient between oil and gas samples at high pressure. Accurate estimation of tortuosity and fluid diffusion is critical for the gas injection strategy in a shale formation. Greater tortuosity and smaller fluid diffusion rate lead to longer injection and production times for desirable economic recovery.

Characterization of laminar flow in periodic open-cell porous structures

The present work deals with the numerical simulations of 3D incompressible flow through periodic porous structures, consisting of cubic cells with different strut geometry and structure tilting with respect to the flow direction. Simulation results are obtained for different porosities, while covering a range of Reynolds numbers from laminar-steady flow (Darcy regime) up to the transition to laminar-unsteady flow (moderate Forchheimer regime). These results are post-processed in order to characterize the influence of the periodic porous structures on the flow statistics related to the Darcy-Forchheimer law. Based on this analysis, along with 3D simulation results previously obtained for different random foams, correlations for the Darcy and Forchheimmer permeability coefficients are developed from a theoretical background, being expressed only as functions of the cell geometrical parameters and tortuosity estimation. However, the influences of flow tortuosity and cell orientation on the Darcy coefficient are found to cancel each other. The proposed correlation for the Darcy coefficient performs very well for both periodic and random porous structures, when compared with recent correlations available in the literature. The performance of the correlation proposed for the Forchheimmer coefficient is found to be satisfactory, however, different correlation constants were found for periodic and random structures. The proposed correlation for the Forchheimer permeability coefficient depends on the flow tortuosity inside the porous structure, which must be estimated either through 3D fluid flow simulations or using tortuosity correlations. In this respect, a correlation is proposed for predicting the flow tortuosity inside porous structures, as an alternative for avoiding 3D simulations.

Estimation of geodesic tortuosity and constrictivity in stationary random closed sets

AbstractWe investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance for the analysis of effective transport properties in porous or composite materials. Loosely speaking, geodesic tortuosity measures the windedness of paths, whereas the notion of constrictivity captures the appearance of bottlenecks resulting from narrow passages within a given materials phase. We first provide mathematically precise definitions of these quantities and introduce appropriate estimators. Then, we show strong consistency of these estimators for unboundedly growing sampling windows. In order to apply our estimators to real data sets, the extent of edge effects needs to be controlled. This is illustrated using a model for a multiphase material that is incorporated in solid oxide fuel cells.

Hydrodynamics of a packed bed of non-spherical polydisperse particles: A fully virtual approach validated by experiments

This work presents a numerical workflow to generate a virtual packed bed made of non-spherical polydisperse particles, and subsequently predict its permeability. Wood chips were taken as an illustration. First, chips are sized before being recreated numerically. Then, using LMGC90, a DEM code, a packed bed made of those chips was generated. Once bed internal had been sampled, CFD tools belonging to the OpenFOAM library were used to mesh the geometry (snappyHexMesh) and compute fluid motion (simpleFoam). Finally, using numerical results, the bed permeability was computed in both Stokes and inertial regimes - turbulence being described by Launder-Reece-Rodi model. In parallel, experimental measurements of the permeability of a packed bed, made of the exact same wood chips, was carried out. These experiments were used as a reference to challenge numerical results. The permeability value delivered by the workflow is 16.0% higher than the experimental value. This value has to be compared with Kozeny-Carman equation estimation which overestimates bed permeability by 115%. Going one step further, this framework was successfully used to compute inertial effects constant of the Forshheimer equation for our packed bed. Throughout this article, a special care has been taken in explaining and evaluating the impact of all the key parameters, namely, number of particles that have to be sized, mesh refinement level, numerical domain dimensions. This workflow opens the door to numerical estimation of bed tortuosity, dispersion coefficients, volumetric heat exchange coefficients, and much more, using the particle size distribution as unique input data.

Computational prediction of nanoscale transport characteristics and catalyst utilization in fuel cell catalyst layers by the lattice Boltzmann method

In the present study, a three-dimensional lattice Boltzmann model based on the quasi-random nanostructural model is proposed to evaluate the mass transport properties and catalyst utilization of fuel cell catalyst layers in pursuance of catalyst performance improvement. A series of catalyst layers is randomly generated with statistical significance at the 95% confidence level to reflect the heterogeneity of the catalyst layer nanostructures. The nanoscale gas transport phenomena inside the catalyst layers are simulated by the D3Q19 (i.e., three-dimensional, 19 velocities) lattice Boltzmann method, and the corresponding mass transport characteristics are mathematically modeled in terms of structural properties. Considering the nanoscale reactant transport phenomena, a transport-based effective catalyst utilization factor is defined and statistically analyzed to determine the structure-transport influence on catalyst utilization. The tortuosity estimation results clearly show that the classic Bruggeman equation underestimates the tortuosity of the catalyst layers and should be modified for PEFC applications. Subsequently, the effective mass diffusion coefficient is calculated by applying the tortuosity factors to the Knudsen diffusion coefficient in the catalyst layers, and it shows good agreement with published experimental data. These results indicate that Knudsen diffusion is the dominant mass transfer mechanism for fuel cell catalyst layers and that the pre-estimated tortuosity accurately reflects the mass transfer phenomena in the catalyst layers. Furthermore, catalyst utilization can be affected by excessive Pt/C catalyst loading due to the lack of pore interconnections, and it is significantly limited by the substantive reactant mass transport path inside the fuel cell catalyst layers.

A three-dimensional model for quantification of the representative elementary volume of tortuosity in granular porous media

For most of aquifers with abundant groundwater resource, quantifications of tortuosity and corresponding representative elementary volume (REV) are very essential to improve the understanding of groundwater and contaminant transfers in porous media. In this study, a mathematical model of tortuosity based on the three dimensional (3D) microstructure of regular tetrahedron (RTM) is proposed to quantify tortuosity and corresponding REV of granular porous media. The calculated tortuosity using the new 3D RTM model agrees well with the measured tortuosity in experiment, indicating that the new 3D microstructure model is more appropriate to precisely delineate the tortuosity of granular porous media. Afterward, the new model is utilized to quantify the tortuosity of heterogeneous translucent silica. Moreover, corresponding REV is estimated using a criterion of relative gradient error (εgi). Results suggest minimum τ-REV sizes most distribute in 0.0–5.0 mm and the bound of cumulative frequency above 80% is larger than 3.00 mm. The REV scale of tortuosity has its own rationality and superiority over that estimated by two-dimensional (2D) tortuosity model, implying the proposed 3D tortuosity model of RTM is helpful for understanding the tortuosity of flow paths in granular porous media and corresponding REV estimation of tortuosity.

A fully automated tortuosity quantification system with application to corneal nerve fibres in confocal microscopy images

Recent clinical research has highlighted important links between a number of diseases and the tortuosity of curvilinear anatomical structures like corneal nerve fibres, suggesting that tortuosity changes might detect early stages of specific conditions. Currently, clinical studies are mainly based on subjective, visual assessment, with limited repeatability and inter-observer agreement. To address these problems, we propose a fully automated framework for image-level tortuosity estimation, consisting of a hybrid segmentation method and a highly adaptable, definition-free tortuosity estimation algorithm. The former combines an appearance model, based on a Scale and Curvature-Invariant Ridge Detector (SCIRD), with a context model, including multi-range learned context filters. The latter is based on a novel tortuosity estimation paradigm in which discriminative, multi-scale features can be automatically learned for specific anatomical objects and diseases. Experimental results on 140 in vivo confocal microscopy images of corneal nerve fibres from healthy and unhealthy subjects demonstrate the excellent performance of our method compared to state-of-the-art approaches and ground truth annotations from 3 expert observers.

Prediction of geohydraulic pore pressure gradient differentials for hydrodynamic assessment of hydrogeological units using geophysical and laboratory techniques: a case study of the coastal sector of Akwa Ibom State, Southern Nigeria

We used borehole-constrained geophysical measurements and laboratory analyses of water samples and hydrogeological unit samples to estimate the basic petrophysical parameters required in the Kozeny-Carman-Bear’s equation. This led to the estimation of hydraulic conductivity, permeability and tortuosity. The evaluation of hydraulic pressure gradient differential and the hydraulic pressure differential was possible through Darcy’s law. Our main objective was to assess the effect of hydraulic pressure gradient differential and that of the hydraulic pressure differential on the hydrodynamic coefficients of economically hydrogeologic units of the study area. The specific constants of water such as density, dynamic viscosity and acceleration due to gravity were all employed in estimating some of the parameters as required in the empirical relations used. Graphical relations were used to predict the generic behaviour between permeability and its dependence, and hydraulic pressure gradient and hydraulic pressure differentials respectively. The results of our analyses show that in arenaceous hydrogeologic units like sands characterised by interconnected/communicating pores, hydraulic pressure differential will be high as the thickness of the saturated unit increases—the precondition for high hydrodynamic activity in the saturated medium. Again, in argillaceous materials, the hydraulic pressure gradient differential is high as it is caused by poor geofluid thickness penetration due to little or no communication between pores. This reduces the hydrodynamic coefficients like porosity and permeability in such hydrogeologic units. The observation of these hydraulic energy parameters in hydrogeologic units could be the physical basis for predicting groundwater flow and a guide to designing geofluid flow modelling programmes in saturated subsurface.

Two-Dimensional Plane for Multi-Scale Quantification of Corneal Subbasal Nerve Tortuosity.

PurposeTo assess the performance of a novel system for automated tortuosity estimation and interpretation.MethodsA supervised strategy (driven by observers' grading) was employed to automatically identify the combination of tortuosity measures (i.e., tortuosity representation) leading to the best agreement with the observers. We investigated 18 tortuosity measures including curvature and density of inflection points, computed at multiple spatial scales. To leverage tortuosity interpretation, we propose the tortuosity plane (TP) onto which each image is mapped. Experiments were carried out on 140 images of subbasal nerve plexus of the central cornea, covering four levels of tortuosity. Three experienced observers graded each image independently.ResultsThe best tortuosity representation was the combination of mean curvature at spatial scales 2 and 5. These tortuosity measures were the axes of the proposed TP (interpretation). The system for tortuosity estimation revealed strong agreement with the observers on a global and per-level basis. The agreement with each observer (Spearman's correlation) was statistically significant (αs = 0.05, P < 0.0001) and higher than that of at least one of the other observers in two out of three cases (ρOUR = 0.7594 versus ρObs3 = 0.7225; ρOUR = 0.8880 versus ρObs1 = 0.8017, ρObs3 = 0.7315). Based on paired-sample t-tests, these improvements were significant (P < 0.001).ConclusionsOur automated system stratifies images by four tortuosity levels (discrete scale) matching or exceeding the accuracy of experienced observers. Of importance, the TP allows the assessment of tortuosity on a two-dimensional continuous scale, thus leading to a finer discrimination among images.

Theoretical study on the amplitude ratio of the seismoelectric field to the Stoneley wave and the formation tortuosity estimation from seismoelectric logs

SUMMARY Seismoelectric logging has potential applications in exploring the porous formation characteristics. In this study, we theoretically address how the amplitudes of the Stoneley wave and its accompanying borehole seismoelectric field depend on the porous formation parameters such as porosity, permeability and tortuosity. We calculate the ratio of the electric field amplitude to the pressure amplitude (REP amplitude) for the low-frequency Stoneley wave of different formations and find that the REP amplitude is sensitive to porosity and tortuosity but insensitive to permeability. To confirm this conclusion, we derive the approximate expression of the REP amplitude in the wavenumber–frequency domain which shows that the REP amplitude is dependent on tortuosity but independent of permeability. This contradicts the result concluded by previous researchers from experiments that the REP amplitude is directly proportional to the permeability. The reason is probably attributed to the fact that the rock samples with different permeabilities typically have different tortuosities. Since the REP amplitude is sensitive to tortuosity, we propose a method of estimating formation tortuosity from seismoelectric logs. It is implemented by using the REP amplitude and the wavenumber of the Stoneley wave at a given frequency when the porosity and the pore fluid viscosity and salinity are known. We test the method by estimating the tortuosities from the synthetic seismoelectric waveforms in different formations. The result shows that the errors relative to the input tortuosities are lower than 5.0percent without considering the uncertainties of other input parameters.

Automatic Evaluation of Plus Disease in Retinopathy of Prematurity

Abnormal dilation and tortuosity of retinal blood vessels are the primary signs of plus disease in retinopathy of prematurity. Timely prognosis could help reduce the delay in treatment and the risk of retinal detachment. Our objectives is to determine whether tortuosity and dilation sufficient for plus disease could be assessed most accurately by considering only arterioles, venules, or both. Tortuosity estimation and width measurement is done using previously proposed methods. Image preprocessing is applied before the two features namely, tortuosity and width of blood vessels are estimated to supply as input parameters for classification using K-means clustering technique. The results are validated by comparing with expert ophthalmologists ground truths. Performance is evaluated based on measures as sensitivity, specificity, predictive values and accuracy. The sensitivity, specificity, positive predictive value, negative predictive value and accuracy values obtained when considering both the arteriolar tortuosity and venous dilation are 85.86%, 90.74%, 88.76%, 88.28% and 88.50% respectively.