An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Volumetric quantification of atherosclerotic plaque in CT considering partial volume effect.

Coronary artery calcification (CAC) is quantified based on a computed tomography (CT) scan image. A calcified region is identified. Modified expectation maximization (MEM) of a statistical model for the calcified and background material is used to estimate the partial calcium content of the voxels. The algorithm limits the region over which MEM is performed. By using MEM, the statistical properties of the model are iteratively updated based on the calculated resultant calcium distribution from the previous iteration. The estimated statistical properties are used to generate a map of the partial calcium content in the calcified region. The volume of calcium in the calcified region is determined based on the map. The experimental results on a cardiac phantom, scanned 90 times using 15 different protocols, demonstrate that the proposed method is less sensitive to partial volume effect and noise, with average error of 9.5% (standard deviation (SD) of 5-7mm(3)) compared with 67% (SD of 3-20mm(3)) for conventional techniques. The high reproducibility of the proposed method for 35 patients, scanned twice using the same protocol at a minimum interval of 10 min, shows that the method provides 2-3 times lower interscan variation than conventional techniques.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Neurally Adjusted Ventilatory Assist (NAVA) improves the matching of diaphragmatic electrical activity and tidal volume in comparison to pressure support (PS) under non invasive ventilation

INTRODUCTION. Patient-ventilator asynchrony is a frequent issue in non invasivemechanical ventilation (NIV) and leaks at the patient-mask interface play a major role in itspathogenesis. NIV algorithms alleviate the deleterious impact of leaks and improve patient-ventilator interaction. Neurally adusted ventilatory assist (NAVA), a neurally triggered modethat avoids interferences between leaks and the usual pneumatic trigger, could further improvepatient-ventilator interaction in NIV patients.OBJECTIVES. To evaluate the feasibility ofNAVAin patients receiving a prophylactic postextubationNIV and to compare the respective impact ofPSVandNAVAwith and withoutNIValgorithm on patient-ventilator interaction.METHODS. Prospective study conducted in 16 beds adult critical care unit (ICU) in a tertiaryuniversity hospital. Over a 2 months period, were included 17 adult medical ICU patientsextubated for less than 2 h and in whom a prophylactic post-extubation NIV was indicated.Patients were randomly mechanically ventilated for 10 min with: PSV without NIV algorithm(PSV-NIV-), PSV with NIV algorithm (PSV-NIV+),NAVAwithout NIV algorithm (NAVANIV-)and NAVA with NIV algorithm (NAVA-NIV+). Breathing pattern descriptors, diaphragmelectrical activity, leaks volume, inspiratory trigger delay (Tdinsp), inspiratory time inexcess (Tiexcess) and the five main asynchronies were quantified. Asynchrony index (AI) andasynchrony index influenced by leaks (AIleaks) were computed.RESULTS. Peak inspiratory pressure and diaphragm electrical activity were similar in thefour conditions. With both PSV and NAVA, NIV algorithm significantly reduced the level ofleak (p\0.01). Tdinsp was not affected by NIV algorithm but was shorter in NAVA than inPSV (p\0.01). Tiexcess was shorter in NAVA and PSV-NIV+ than in PSV-NIV- (p\0.05).The prevalence of double triggering was significantly lower in PSV-NIV+ than in NAVANIV+.As compared to PSV,NAVAsignificantly reduced the prevalence of premature cyclingand late cycling while NIV algorithm did not influenced premature cycling. AI was not affectedby NIV algorithm but was significantly lower in NAVA than in PSV (p\0.05). AIleaks wasquasi null with NAVA and significantly lower than in PSV (p\0.05).CONCLUSIONS. NAVA is feasible in patients receiving a post-extubation prophylacticNIV. NAVA and NIV improve patient-ventilator synchrony in different manners. NAVANIV+offers the best patient-ventilator interaction. Clinical studies are required to assess thepotential clinical benefit of NAVA in patients receiving NIV.

Modeling complex wells with the multi-scale finite-volume method

In this paper, an extension of the multi-scale finite-volume (MSFV) method is devised, which allows to Simulate flow and transport in reservoirs with complex well configurations. The new framework fits nicely into the data Structure of the original MSFV method,and has the important property that large patches covering the whole well are not required. For each well. an additional degree of freedom is introduced. While the treatment of pressure-constraint wells is trivial (the well-bore reference pressure is explicitly specified), additional equations have to be solved to obtain the unknown well-bore pressure of rate-constraint wells. Numerical Simulations of test cases with multiple complex wells demonstrate the ability of the new algorithm to capture the interference between the various wells and the reservoir accurately. (c) 2008 Elsevier Inc. All rights reserved.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

A multilevel multiscale finite volume method

The Multiscale Finite Volume (MsFV) method has been developed to efficiently solve reservoir-scale problems while conserving fine-scale details. The method employs two grid levels: a fine grid and a coarse grid. The latter is used to calculate a coarse solution to the original problem, which is interpolated to the fine mesh. The coarse system is constructed from the fine-scale problem using restriction and prolongation operators that are obtained by introducing appropriate localization assumptions. Through a successive reconstruction step, the MsFV method is able to provide an approximate, but fully conservative fine-scale velocity field. For very large problems (e.g. one billion cell model), a two-level algorithm can remain computational expensive. Depending on the upscaling factor, the computational expense comes either from the costs associated with the solution of the coarse problem or from the construction of the local interpolators (basis functions). To ensure numerical efficiency in the former case, the MsFV concept can be reapplied to the coarse problem, leading to a new, coarser level of discretization. One challenge in the use of a multilevel MsFV technique is to find an efficient reconstruction step to obtain a conservative fine-scale velocity field. In this work, we introduce a three-level Multiscale Finite Volume method (MlMsFV) and give a detailed description of the reconstruction step. Complexity analyses of the original MsFV method and the new MlMsFV method are discussed, and their performances in terms of accuracy and efficiency are compared.

An evaluation of volume-based morphometry for prediction of mild cognitive impairment and Alzheimer's disease.

Voxel-based morphometry from conventional T1-weighted images has proved effective to quantify Alzheimer's disease (AD) related brain atrophy and to enable fairly accurate automated classification of AD patients, mild cognitive impaired patients (MCI) and elderly controls. Little is known, however, about the classification power of volume-based morphometry, where features of interest consist of a few brain structure volumes (e.g. hippocampi, lobes, ventricles) as opposed to hundreds of thousands of voxel-wise gray matter concentrations. In this work, we experimentally evaluate two distinct volume-based morphometry algorithms (FreeSurfer and an in-house algorithm called MorphoBox) for automatic disease classification on a standardized data set from the Alzheimer's Disease Neuroimaging Initiative. Results indicate that both algorithms achieve classification accuracy comparable to the conventional whole-brain voxel-based morphometry pipeline using SPM for AD vs elderly controls and MCI vs controls, and higher accuracy for classification of AD vs MCI and early vs late AD converters, thereby demonstrating the potential of volume-based morphometry to assist diagnosis of mild cognitive impairment and Alzheimer's disease.

An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

A structural MRI study of motor conversion disorder: evidence of reduction in thalamic volume.

OBJECTIVE: To investigate potential abnormalities in subcortical brain structures in conversion disorder (CD) compared with controls using a region of interest (ROI) approach. METHODS: Fourteen patients with motor CD were compared with 31 healthy controls using high-resolution MRI scans with an ROI approach focusing on the basal ganglia, thalamus and amygdala. Brain volumes were measured using Freesurfer, a validated segmentation algorithm. RESULTS: Significantly smaller left thalamic volumes were found in patients compared with controls when corrected for intracranial volume. These reductions did not vary with handedness, laterality, duration or severity of symptoms. CONCLUSIONS: These differences may reflect a primary disease process in this area or be secondary effects of the disorder, for example, resulting from limb disuse. Larger, longitudinal structural imaging studies will be required to confirm the findings and explore whether they are primary or secondary to CD.

An efficient total variation algorithm for super-resolution in fetal brain MRI with adaptive regularization.

Although fetal anatomy can be adequately viewed in new multi-slice MR images, many critical limitations remain for quantitative data analysis. To this end, several research groups have recently developed advanced image processing methods, often denoted by super-resolution (SR) techniques, to reconstruct from a set of clinical low-resolution (LR) images, a high-resolution (HR) motion-free volume. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has been quite attracted by Total Variation energies because of their ability in edge preserving but only standard explicit steepest gradient techniques have been applied for optimization. In a preliminary work, it has been shown that novel fast convex optimization techniques could be successfully applied to design an efficient Total Variation optimization algorithm for the super-resolution problem. In this work, two major contributions are presented. Firstly, we will briefly review the Bayesian and Variational dual formulations of current state-of-the-art methods dedicated to fetal MRI reconstruction. Secondly, we present an extensive quantitative evaluation of our SR algorithm previously introduced on both simulated fetal and real clinical data (with both normal and pathological subjects). Specifically, we study the robustness of regularization terms in front of residual registration errors and we also present a novel strategy for automatically select the weight of the regularization as regards the data fidelity term. Our results show that our TV implementation is highly robust in front of motion artifacts and that it offers the best trade-off between speed and accuracy for fetal MRI recovery as in comparison with state-of-the art methods.

Glucose-dependent insulinotropic polypeptide receptor deficiency leads to modifications of trabecular bone volume and quality in mice.

A role for the gastro-intestinal tract in controlling bone remodeling is suspected since serum levels of bone remodeling markers are affected rapidly after a meal. Glucose-dependent insulinotropic polypeptide (GIP) represents a suitable candidate in mediating this effect. The aim of the present study was to investigate the effect of total inhibition of GIP signaling on trabecular bone volume, microarchitecture and quality. We used GIP receptor (GIPR) knockout mice and investigated trabecular bone volume and microarchitecture by microCT and histomorphometry. GIPR-deficient animals at 16 weeks of age presented with a significant (20%) increase in trabecular bone mass accompanied by an increase (17%) in trabecular number. In addition, the number of osteoclasts and bone formation rate was significantly reduced and augmented, respectively in these animals when compared with wild-type littermates. These modifications of trabecular bone microarchitecture are linked to a remodeling in the expression pattern of adipokines in the GIPR-deficient mice. On the other hand, despite significant enhancement in bone volume, intrinsic mechanical properties of the bone matrix was reduced as well as the distribution of bone mineral density and the ratio of mature/immature collagen cross-links. Taken together, these results indicate an increase in trabecular bone volume in GIPR KO animals associated with a reduction in bone quality.

International Society of Urological Pathology (ISUP) Consensus Conference on Handling and Staging of Radical Prostatectomy Specimens. Working group 2: T2 substaging and prostate cancer volume.

The 2009 International Society of Urological Pathology consensus conference in Boston made recommendations regarding the standardization of pathology reporting of radical prostatectomy specimens. Issues relating to the substaging of pT2 prostate cancers according to the TNM 2002/2010 system, reporting of tumor size/volume and zonal location of prostate cancers were coordinated by working group 2. A survey circulated before the consensus conference demonstrated that 74% of the 157 participants considered pT2 substaging of prostate cancer to be of clinical and/or academic relevance. The survey also revealed a considerable variation in the frequency of reporting of pT2b substage prostate cancer, which was likely a consequence of the variable methodologies used to distinguish pT2a from pT2b tumors. Overview of the literature indicates that current pT2 substaging criteria lack clinical relevance and the majority (65.5%) of conference attendees wished to discontinue pT2 substaging. Therefore, the consensus was that reporting of pT2 substages should, at present, be optional. Several studies have shown that prostate cancer volume is significantly correlated with other clinicopathological features, including Gleason score and extraprostatic extension of tumor; however, most studies fail to demonstrate this to have prognostic significance on multivariate analysis. Consensus was reached with regard to the reporting of some quantitative measure of the volume of tumor in a prostatectomy specimen, without prescribing a specific methodology. Incorporation of the zonal and/or anterior location of the dominant/index tumor in the pathology report was accepted by most participants, but a formal definition of the identifying features of the dominant/index tumor remained undecided.

NAVA enhances tidal volume and diaphragmatic electro-myographic activity matching: a Range90 analysis of supply and demand.

Neurally adjusted ventilatory assist (NAVA) is a ventilation assist mode that delivers pressure in proportionality to electrical activity of the diaphragm (Eadi). Compared to pressure support ventilation (PS), it improves patient-ventilator synchrony and should allow a better expression of patient's intrinsic respiratory variability. We hypothesize that NAVA provides better matching in ventilator tidal volume (Vt) to patients inspiratory demand. 22 patients with acute respiratory failure, ventilated with PS were included in the study. A comparative study was carried out between PS and NAVA, with NAVA gain ensuring the same peak airway pressure as PS. Robust coefficients of variation (CVR) for Eadi and Vt were compared for each mode. The integral of Eadi (ʃEadi) was used to represent patient's inspiratory demand. To evaluate tidal volume and patient's demand matching, Range90 = 5-95 % range of the Vt/ʃEadi ratio was calculated, to normalize and compare differences in demand within and between patients and modes. In this study, peak Eadi and ʃEadi are correlated with median correlation of coefficients, R > 0.95. Median ʃEadi, Vt, neural inspiratory time (Ti_ ( Neural )), inspiratory time (Ti) and peak inspiratory pressure (PIP) were similar in PS and NAVA. However, it was found that individual patients have higher or smaller ʃEadi, Vt, Ti_ ( Neural ), Ti and PIP. CVR analysis showed greater Vt variability for NAVA (p < 0.005). Range90 was lower for NAVA than PS for 21 of 22 patients. NAVA provided better matching of Vt to ʃEadi for 21 of 22 patients, and provided greater variability Vt. These results were achieved regardless of differences in ventilatory demand (Eadi) between patients and modes.

Factors associated with 24-hour urinary volume: the Swiss salt survey.

BACKGROUND: Low 24-hour urine volume (24 UV) may be a significant risk factor for decline in kidney function. We therefore aimed to study associated markers and possible determinants of 24 UV in a sample of the Swiss population. METHODS: The cross-sectional Swiss Salt Study included a population-based sample of 1535 (746 men and 789 women) individuals from three linguistic regions of Switzerland. Data from 1300 subjects were available for the present analysis. 24 UV was measured using 24-hour urine collection. Determinants of 24 UV were identified using multivariable linear regression models. RESULTS: In bivariate analysis, 24 UV was higher in women compared to men (2000 ml/24 h [interquartile range (IQR): 1354, 2562] versus 1780 ml/24 h [IQR: 1244, 2360], p = 0.002). In multivariable regression analyses, independent associated markers of 24 UV were female sex (β = 280, 95% confidence interval [CI]: 174, 386, p < 0.0001), fluid intake (β = 604, 95% CI: 539, 670, p < 0.0001), sodium excretion (β = 4.2, 95% CI: 3.4, 4.9, p < 0.0001) age (β = 6.6, CI: 3.4, 9.7, p < .0001), creatinine clearance (β = 2.4, CI: 0.2, 4.6, p = 0.04), living in the German-speaking part of Switzerland (β = 124, CI: 29, 219, p = 0.01), alcohol consumption (β = 41, CI: 9, 73, p = 0.01 for increasing categories of alcohol consumption), body mass index (β = -32, CI: -45, -18, p < 0.0001), current smoking (β = -146, CI: -265, -26, p = 0.02), and consumption of meat and cold cut (β = -56, CI: -108, -5, p = 0.03). CONCLUSION: In this large population-based, cross-sectional study, we found several strong and independent correlates for 24 UV. These findings may be important to improve our understanding in the development of chronic kidney disease.