Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Effect of material anisotropy on the onset of convective flow in three-dimensional fluid-saturated faults

In order to investigate the effect of material anisotropy on convective instability of three-dimensional fluid-saturated faults, an exact analytical solution for the critical Rayleigh number of three-dimensional convective flow has been obtained. Using this critical Rayleigh number, effects of different permeability ratios and thermal conductivity ratios on convective instability of a vertically oriented three-dimensional fault have been examined in detail. It has been recognized that (1) if the fault material is isotropic in the horizontal direction, the horizontal to vertical permeability ratio has a significant effect on the critical Rayleigh number of the three-dimensional fault system, but the horizontal to vertical thermal conductivity ratio has little influence on the convective instability of the system, and (2) if the fault material is isotropic in the fault plane, the thermal conductivity ratio of the fault normal to plane has a considerable effect on the critical Rayleigh number of the three-dimensional fault system, but the effect of the permeability ratio of the fault normal to plane on the critical Rayleigh number of three-dimensional convective flow is negligible.

Characterisation of the three-dimensional structure of earthworm burrow systems using image analysis and mathematical morphology

The aim of this work was to exemplify the specific contribution of both two- and three-dimensional (31)) X-ray computed tomography to characterise earthworm burrow systems. To achieve this purpose we used 3D mathematical morphology operators to characterise burrow systems resulting from the activity of an anecic (Aporrectodea noctunia), and an endogeic species (Allolobophora chlorotica), when both species were introduced either separately or together into artificial soil cores. Images of these soil cores were obtained using a medical X-ray tomography scanner. Three-dimensional reconstructions of burrow systems were obtained using a specifically developed segmentation algorithm. To study the differences between burrow systems, a set of classical tools of mathematical morphology (granulometries) were used. So-called granulometries based on different structuring elements clearly separated the different burrow systems. They enabled us to show that burrows made by the anecic species were fatter, longer, more vertical, more continuous but less sinuous than burrows of the endogeic species. The granulometry transform of the soil matrix showed that burrows made by A. nocturna were more evenly distributed than those of A. chlorotica. Although a good discrimination was possible when only one species was introduced into the soil cores, it was not possible to separate burrows of the two species from each other in cases where species were introduced into the same soil core. This limitation, partly due to the insufficient spatial resolution of the medical scanner, precluded the use of the morphological operators to study putative interactions between the two species.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

Standard Values for Real-Time Transthoracic Three-Dimensional Echocardiographic Dyssynchrony Indexes in a Normal Population

Background: There is a paucity of information describing the real-time 3-dimensional echocardiography (RT3DE) and dyssynchrony indexes (DIs) of a normal population. We evaluate the RT3DE DIs in a population with normal electrocardiograms and 2- and 3-dimensional echocardiographic analyses. This information is relevant for cardiac resynchronization therapy. Methods: We evaluated 131 healthy volunteers (73 were male, aged 46 +/- 14 years) who were referred for routine echocardiography; who presented normal cardiac structure on electrocardiography, 2-dimensional echocardiography, and RT3DE; and who had no history of cardiac diseases. We analyzed 3-dimensional left ventricular ejection fraction, left ventricle end-diastolic volume, left ventricle end-systolic volume, and left ventricular systolic DI% (6-, 12-, and 16-segment models). RT3DE data were analyzed by quantifying the statistical distribution (mean, median, standard deviation [SD], relative SD, coefficient of skewness, coefficient of kurtosis, Kolmogorov-Smirnov test, D`Agostino-Pearson test, percentiles, and 95% confidence interval). Results: Left ventricular ejection fraction ranged from 50% to 80% (66.1% +/- 7.1%); left ventricle end-diastolic volume ranged from 39.8 to 145 mL (79.1 +/- 24.9 mL); left ventricle end-systolic volume ranged from 12.9 to 66 mL (27 +/- 12.1 mL); 6-segment DI% ranged from 0.20% to 3.80% (1.21% +/- 0.66%), median: 1.06, relative SD: 0.5482, coefficient of skewness: 1.2620 (P < .0001), coefficient of Kurtosis: 1.9956 (P = .0039); percentile 2.5%: 0.2900, percentile 97.5%: 2.8300; 12-segment DI% ranged from 0.22% to 4.01% (1.29% +/- 0.71%), median: 1.14, relative SD: 0.95, coefficient of skewness: 1.1089 (P < .0001), coefficient of Kurtosis: 1.6372 (P = .0100), percentile 2.5%: 0.2850, percentile 97.5%: 3.0700; and 16-segment DI% ranged from 0.29% to 4.88% (1.59 +/- 0.99), median: 1.39, relative SD: 0.56, coefficient of skewness: 1.0792 (P < .0001), coefficient of Kurtosis: 0.9248 (P = .07), percentile 2.5%: 0.3750, percentile 97.5%: 3.750. Conclusion: This study allows for the quantification of RT3DE DIs in normal subjects, providing a comparison for patients with heart failure who may be candidates for cardiac resynchronization therapy. (J Am Soc Echocardiogr 2008; 21: 1229-1235)

Value of real time three-dimensional echocardiography in patients with hypertrophic cardiomyopathy: Comparison with two-dimensional echocardiography and magnetic resonance imaging

Real time three-dimensional echocardiography (RT3DE) has been demonstrated to be an accurate technique to quantify left ventricular (LV) volumes and function in different patient populations. We sought to determine the value of RT3DE for evaluating patients with hypertrophic cardiomyopathy (HCM), in comparison with cardiac magnetic resonance imaging (MRI). Methods: We studied 20 consecutive patients with HCM who underwent two-dimensional echocardiography (2DE), RT3DE, and MRI. Parameters analyzed by echocardiography and MRI included: wall thickness, LV volumes, ejection fraction (LVEF), mass, geometric index, and dyssynchrony index. Statistical analysis was performed by Lin agreement coefficient, Pearson linear correlation and Bland-Altman model. Results: There was excellent agreement between 2DE and RT3DE (Rc = 0.92), 2DE and MRI (Rc = 0.85), and RT3DE and MRI (Rc = 0.90) for linear measurements. Agreement indexes for LV end-diastolic and end-systolic volumes were Rc = 0.91 and Rc = 0.91 between 2DE and RT3DE, Rc = 0.94 and Rc = 0.95 between RT3DE and MRI, and Rc = 0.89 and Rc = 0.88 between 2DE and MRI, respectively. Satisfactory agreement was observed between 2DE and RT3DE (Rc = 0.75), RT3DE and MRI (Rc = 0.83), and 2DE and MRI (Rc = 0.73) for determining LVEF, with a mild underestimation of LVEF by 2DE, and smaller variability between RT3DE and MRI. Regarding LV mass, excellent agreement was observed between RT3DE and MRI (Rc = 0.96), with bias of -6.3 g (limits of concordance = 42.22 to -54.73 g). Conclusion: In patients with HCM, RT3DE demonstrated superior performance than 2DE for the evaluation of myocardial hypertrophy, LV volumes, LVEF, and LV mass.

Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.

Three-dimensional electrical impedance, tomography: A topology optimization approach

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

Microsurgical Anatomy of the Posterior Cerebral Artery in Three-Dimensional Images

OBJECTIVE: To describe the microsurgical anatomy, branches, and anatomic relationships of the posterior cerebral artery (PCA) represented in three-dimensional images. METHODS: Seventy hemispheres of 35 brain specimens were studied. They were previously injected with red silicone and fixed in 10% formalin for at least 40 days. Four of the studied specimens were frozen at -10 degrees to -15 degrees C for 14 days, and additional dissection was done with the Klingler`s fiber dissection technique at x6 to x40 magnification. Each segment of the artery was measured and photographed to obtain three-dimensional stereoscopic images. RESULTS: The PCA origin was in the interpeduncular cistern at the pontomesencephalic junction level in 23 specimens (65.7%). The PCA was divided into four segments: P1 extends from the PCA origin to its junction with the posterior communicating artery with an average length of 7.7 mm; P2 was divided into an anterior and posterior segment. The P2A segment begins at the posterior communicating artery and ends at the most lateral aspect of the cerebral peduncle, with an average length of 23.6 mm, and the P2P segment extends from the most lateral aspect of the cerebral peduncle to the posterior edge of the lateral surface of the midbrain, with an average length of 16.4 mm; P3 extends from the posterior edge of the lateral surface of the midbrain and ends at the origin of the parieto-occipital sulcus along the calcarine fissure, with an average length of 19.8 mm; and the P4 segment corresponds to the parts of the PCA that run along or inside both the parieto-occipital sulcus and the distal part of the calcarine fissure. CONCLUSIONS: To standardize the neurosurgical practice and knowledge, surgical anatomic classifications should be used uniformly and further modified according to the neurosurgical experience gathered. The PCA classification proposed intends to correlate its anatomic segments with their required microneurosurgical approaches.

Quantitative Analysis of Placental Vasculature by Three-Dimensional Power Doppler Ultrasonography in Normal Pregnancies From 12 to 40 Weeks of Gestation

Evaluate the distribution and variation of placental vascular indices according to gestational age and placental volume. From March to November 2007, three-dimensional (3D)-power Doppler ultrasound was performed in 295 normal pregnancies from 12 to 40 weeks of gestation. Using the same preestablished settings for all patients, power Doppler was applied to the placenta and placental Volume was obtained by the rotational technique (VOCAL(TM)). The 3D-power histogram was used to determine the placental vascular indices: vascularization index (VI), flow index (FI) and vascularization-flow index (VFI). The placental vascular indices were then plotted against gestational age and placental volume. All placental vascular indices showed constant distribution throughout gestation. A tendency for a reduction in placental vascular indices with increased placental volume was observed, but was only statistically significant when placental FI was considered (p < 0.05). All placental vascular indices estimated by 3D-power Doppler ultrasonography presented constant distribution throughout gestation, despite the increase in placental volume according to gestational age. (C) 2008 Elsevier Ltd. All rights reserved.

Three-dimensional sonographic measurement of contralateral lung volume in fetuses with isolated congenital diaphragmatic hernia

Purpose. To use 3-dimensional sonography (3DUS) to measure contralateral lung volume and evaluate the potential of this measurement to predict neonatal outcome in isolated congenital diaphragmatic hernia (CDH). Methods. Between January 2002 and December 2004, the contralateral lung volumes of 39 fetuses with isolated CDH were measured via 3DUS using rotational multiplanar imaging. The observed/expected contralateral fetal lung volume ratios (o/eContFLVR) were compared with the lung/head ratio (LHR), observed/expected total fetal lung volume ratio (o/e-TotFLVR), and postnatal outcome. Results. Contralateral lung volumes are less reduced than total lung volumes in CDH. The bias and precision of 3DUS in estimating contralateral lung volumes were 0.99 cm(3) and 1.11 cm(3), respectively, with absolute limits of agreement ranging from -1.19 cm(3) to + 3.17 cm(3). The o/e-ContFLVR was significantly lower in neonatal death cases (median, 0.49 cm(3); range, 0.22-0.99 cm(3)) than in survival cases (median, 0.58 cm(3); range, 0.42-0.92 cm(3) [p < 0.011). Overall accuracy of the o/e-ContFLVR, o/e-TotFLVR, and LHR in predicting neonatal death were 67.7% (21/31), 80.7% (25/31), and 77.4% (24/31), respectively. Conclusion. Although o/e-ContFLVR can be precisely measured with 3DUS and can be used to predict neonatal death in CDH, it is less accurate than LHR and o/e-TotFLVR for that purpose. (C) 2007 Wiley Periodicals, Inc.

Prenatal diagnosis of posterior mediastinal lymphangioma by two- and three-dimensional ultrasonography

Lymphangioma is a rare benign tumor characterized by proliferating lymph vessels and composed of large cyst spaces with endothelium-lined channels of varying dimensions. The incidence of lymphangioma is approximately one in 6000 pregnancies. Less than 1 % of lymphangiomas are purely mediastinal. The great majority of cases are of cystic lymphangioma, but very rarely there is a mixed lesion consisting of multiple cysts of dilated capillary and lymph vessels. We report a case of posterior mediastinal lymphangioma diagnosed at 28 weeks` gestation, in which three-dimensional ultrasonography was helpful in determining the precise location of the tumor. A Cesarean section was performed at 39 weeks and the tumor was resected on the 5(th) day postdelivery; histological examination revealed a mixed cystic lymphangioma. Copyright (C) 2008 ISUOG. Published by John Wiley & Sons, Ltd.

Ipsilateral Lung Volumes Assessed by Three-Dimensional Ultrasonography in Fetuses with Isolated Congenital Diaphragmatic Hernia

Objective: To evaluate the precision of three-dimensional ultrasonography (3DUS) in estimating the ipsilateral lung volume and the potential of this measurement to predict neonatal death in congenital diaphragmatic hernia (CDH). Methods: Between January 2002 and December 2004, the ipsilateral lung volumes were assessed by 3DUS using the technique of rotation of the multiplan imaging in 39 fetuses with CDH. The observed/ expected ipsilateral lung volume ratios (o/e-IpsiFLVR) were compared to the lung/head ratios (LHR) and to the observed/ expected total fetal lung volume ratios (o/e-TotFLVR) as well as to postnatal death. Results: Ipsilateral lung volumes (median 0.12, range 0.01-0.66) were more reduced than the total lung volumes (median 0.52, range 0.11-0.95, p < 0.001) in CDH. The bias and precision of 3DUS in estimating ipsilateral lung volumes were -0.61 and 0.99 cm 3, respectively, with absolute limits of agreement from -2.56 to +1.33 cm(3). The o/e-IpsiFLVR was lower in neonatal death cases (median 0.09, range 0.01-0.46) than in survivals (median 0.18, range 0.01-0.66), but this difference was not statistically significance (p > 0.05). The sensitivity, speci-ficity, (positive and negative) predictive values and accuracy of o/e-IpsiFLVR in predicting neonatal death was 52.6% (10/19), 83.3% (10/12), 83.3% (10/12), 52.6% (10/19) and 64.5% (20/31), respectively. Conclusion: Although the ipsilateral lung volume can be measured by 3DUS, it cannot be used to predict neonatal death when considering it alone. However, it is important to measure it to calculate the total fetal lung volumes as the o/e-TotFLVR has the best efficacy in predicting neonatal death in isolated CDH. Copyright (C) 2008 S. Karger AG, Basel

Are the recommendations from three-dimensional gait analysis associated with better postoperative outcomes in patients with cerebral palsy?

This study was performed to check if recommendations based on three-dimensional gait analysis (3DGA) are associated with better postoperative outcomes in patients with cerebral palsy (CP). Thirty-eight patients who underwent orthopedic surgery and assessment at the Gait Analysis Laboratory were evaluated retrospectively. The patients were divided in four groups according to the agreement between the recommendations from gait analysis and the procedures actually carried out. Fifteen patients with diplegic spastic cerebral palsy and indication for orthopedic surgery to improve walking - and whose surgical intervention was postponed - were also included in the study as a control group. Fourteen gait parameters recorded before and after treatment, were included in the statistical analysis. No gait improvement was noted in the control group or inh patients on whom no procedures recommended by the gait exam were performed (agreement of 0%). In the other groups, agreements averaged 46.71%, 72.2%, and 100%, respectively. Improvement of gait parameters after treatment was observed in these groups, with more significant values directly related to increased agreement percentage. Therefore, in this study the patients whose treatment matched the recommendations from three-dimensional gait analysis showed a more significant improvement in walking. (c) 2008 Elsevier B.V. All rights reserved.