Mass Preserving Research Articles

SU‐F‐BRF‐06: Density Correction for Deformable Image Registration to Improve CT Number Mapping

Purpose:To improve the accuracy of CT number mapping inside the lung using deformable image registration for cases having substantially large lung volume differences.Methods:The deep‐inspiration‐breath‐hold (DIBH) CT image and the end‐of‐exhalation (EE) phase image in 4DCT of three thoracic cancer patients were enrolled in this study. The lung volumes were manually delineated and the lung volume ratio of DIBH‐CT over EECT is 1.7, 1.8, and 2.0 respectively, demonstrating large volume differences. A demons‐based deformable registration was first applied to register the EECT to the DIBH‐CT for each patient, and the resulting deformation field deformed the EE‐CT image to the DIBH‐CT space. Based on the assumption that the mass of lung remains the same during respiration, we created a mass preserving model to correlate the lung density variations with the lung volumetric changes, which were characterized by the Jacobian derived from the deformation field. The Jacobian is used to correct the lung CT number transferred from the EE‐CT image. The deformed images with and without the density correction were compared using absolute intensity difference created by subtracting the deformed image from the DIBH‐CT image.Results:The deformable registration could register the lung shape very well, but the CT numbers inside the lung could not be registered correctly. Without density correction, the mean and standard deviation of the absolute CT number difference inside the lung were 59±48, 69±49, and 71±42 for the three cases. After density correction, these numbers changed to 18±35, 20±35, and 14±29, respectively, demonstrating an improvement in the accuracy of CT number mapping. The accumulative histogram of the intensity difference also showed that density correction improved CT number mapping.Conclusion:Density correction improved the CT number mapping inside the lung using deformable image registration for difficult cases having large lung volume differences.This work is partially supported by the CPRIT (Cancer Prevention Research Institute of Texas) grant RP110732.

Spectral analysis and long-time behaviour of a Fokker-Planck equation with a non-local perturbation

In this article we consider a Fokker-Planck equation on \mathbb R^d with a non-local, mass preserving perturbation. We first give a spectral analysis of the unperturbed Fokker-Planck operator in an exponentially weighted L^2 -space. In this space the perturbed Fokker-Planck operator is an isospectral deformation of the Fokker-Planck operator, i.e. the spectrum of the Fokker-Planck operator is not changed by the perturbation. In particular, there still exists a unique (normalized) stationary solution of the perturbed evolution equation. Moreover, the perturbed Fokker-Planck operator generates a strongly continuous semigroup of bounded operators. Any solution of the perturbed equation converges towards the stationary state with exponential rate -1 , the same rate as for the unperturbed Fokker-Planck equation. Moreover, for any k\in\mathbb N there exists an invariant subspace with codimension k (if d=1 ) in which the exponential decay rate of the semigroup equals -k .

Bisphosphonates for the Prevention and Treatment of Osteoporosis in Patients with Rheumatic Diseases: A Systematic Review and Meta-Analysis

BackgroundWhile bisphosphonates (BPs) are commonly used in clinical treatment for osteoporosis, their roles on osteoporosis treatment for rheumatic patients remain unclear. We performed a meta-analysis to evaluate the efficacy of BPs on fractures prevention and bone mass preserving in rheumatic patients.Methodology/Principal FindingsWe searched PubMed, EmBase, and the Cochrane Central Register of Controlled Trials for relevant literatures with a time limit of Jan. 6, 2012. All randomized clinical trials of BPs for adult rheumatic patients with a follow-up of 6 months or more were included. We calculated relative risks (RRs) for fractures and weighted mean difference (WMD) for percent change of bone mineral density (BMD). Twenty trials were included for analysis. The RR in rheumatic patients treated with BPs was 0.61 (95%CI [0.44, 0.83], P = 0.002) for vertebral fractures, and 0.49 (95%CI [0.23, 1.02], P = 0.06) for non-vertebral fractures. The WMD of BMD change in the lumbar spine was 3.72% (95%CI [2.72, 4.72], P<0.001) at 6 months, 3.67% (95%CI [2.84, 4.50], P<0.001) at 12 months, 3.64% (95%CI [2.59, 4.69], P<0.001) at 24 months, and 5.87% (95%CI [4.59, 7.15], P<0.001) at 36 months in patients using BPs, as compared with those treated with calcium, vitamin D or calcitonin. In subgroup analyses, rheumatic patients using BPs for osteoporosis prevention had greater WMD than those using BPs for treating osteoporosis at 6 months (4.53% vs. 2.73%, P = 0.05) and 12 months (4.93% vs. 2.91%, P = 0.01).Conclusions/SignificanceIn both short-term and middle-term, BPs can preserve bone mass and reduce the incidence of vertebral fractures in rheumatic patients, mainly for those who have GC consumption. The efficacy of BPs is better when using BPs to prevent rather than to treat osteoporosis in rheumatic patients.

A mass conservation‐based optical flow method for cardiac motion correction in 3D‐PET

Cardiac positron emission tomography (PET) images usually show two kinds of artifacts: the limited resolution of PET leads to partial volume effects and the motion of the heart induces blurring. These phenomena degrade the PET images and induce errors in the quantification. One method of reducing this problem is to use gated PET data. However, the reduction of information per phase leads to an increase in noise on the reconstructed images. Alternatively, the PET data have to be corrected for motion and partial volume effects. Optical flow methods have been shown to accurately estimate the motion between PET image frames. These methods assume that the brightness of the objects remains constant between the frames. This condition is not fulfilled in cardiac PET data because the brightness of the cardiac muscle tissue (myocardium) is not accurately resolved due to the partial volume effect. Therefore, the use of a newly developed optical flow method based upon the conservation of mass condition is proposed to correct the cardiac PET data. Mass conservation is applicable to PET images as the total activity in the field of view may be assumed to remain almost constant, if the data are precorrected for radioactive decay. Two variants of the method using the quadratic and the nonquadratic penalization are presented. The methods were evaluated with respect to correlation coefficient, myocardial thickness and the blood pool activity in the left ventricle on phantom data and on 14 patient image volumes. The proposed methods showed that the cardiac motion can be efficiently corrected despite partial volume effects. The correlation coefficient between the image volumes increased from 0.87 to 0.98 on average. The change in myocardial thickness was reduced from 28% to 3%. The variation in blood pool activity was reduced from 80% to 8%. The algorithm needed only about 4 s for execution. A mass preserving optical flow method of cardiac motion correction in 3D PET data has been presented and tested on phantom as well as patient data. The results show that the motion was corrected for all datasets effectively.

Mass preserving image registration for lung CT

This paper presents a mass preserving image registration algorithm for lung CT images. To account for the local change in lung tissue intensity during the breathing cycle, a tissue appearance model based on the principle of preservation of total lung mass is proposed. This model is incorporated into a standard image registration framework with a composition of a global affine and several free-form B-Spline transformations with increasing grid resolution. The proposed mass preserving registration method is compared to registration using the sum of squared intensity differences as a similarity function on four groups of data: 44 pairs of longitudinal inspiratory chest CT scans with small difference in lung volume; 44 pairs of longitudinal inspiratory chest CT scans with large difference in lung volume; 16 pairs of expiratory and inspiratory CT scans; and 5 pairs of images extracted at end exhale and end inhale phases of 4D-CT images. Registration errors, measured as the average distance between vessel tree centerlines in the matched images, are significantly lower for the proposed mass preserving image registration method in the second, third and fourth group, while there is no statistically significant difference between the two methods in the first group. Target registration error, assessed via a set of manually annotated landmarks in the last group, was significantly smaller for the proposed registration method.

Disaggregation of legacy soil data using area to point kriging for mapping soil organic carbon at the regional scale

Legacy data in the form of soil maps, which often have typical property measurements associated with each polygon, can be an important source of information for digital soil mapping (DSM). Methods of disaggregating such information and using it for quantitative estimation of soil properties by methods such as regression kriging (RK) are needed. Several disaggregation processes have been investigated; preferred methods include those which include consideration of scorpan factors and those which are mass preserving (pycnophylactic) making transitions between different scales of investigation more theoretically sound. Area to point kriging (AtoP kriging) is pycnophylactic and here we investigate its merits for disaggregating legacy data from soil polygon maps. Area to point regression kriging (AtoP RK) which incorporates ancillary data into the disaggregation process was also applied. The AtoP kriging and AtoP RK approaches do not involve collection of new soil measurements and are compared with disaggregation by simple rasterization. Of the disaggregation methods investigated, AtoP RK gave the most accurate predictions of soil organic carbon (SOC) concentrations (smaller mean absolute errors (MAEs) of cross-validation) for disaggregation of soil polygon data across the whole of Northern Ireland.Legacy soil polygon data disaggregated by AtoP kriging and simple rasterization were used in a RK framework for estimating soil organic carbon (SOC) concentrations across the whole of Northern Ireland, using soil sample data from the Tellus survey of Northern Ireland and with other covariates (altitude and airborne radiometric potassium). This allowed direct comparison with previous analysis of the Tellus survey data. Incorporating the legacy data, whether from simple rasterization of the polygons or AtoP kriging, substantially reduced the MAEs of RK compared with previous analyses of the Tellus data. However, using legacy data disaggregated by AtoP kriging in RK resulted in a greater reduction in MAEs. A jack-knife procedure was also performed to determine a suitable number of additional soil samples that would need to be collected for RK of SOC for the whole of Northern Ireland depending on the availability of ancillary data. We recommend i) if only legacy soil polygon map data are available, they should be disaggregated using AtoP kriging, ii) if ancillary data are also available legacy data should be disaggregated using AtoP RK and iii) if new soil measurements are available in addition to ancillary and legacy soil map data, the legacy soil map data should be first disaggregated using AtoP kriging and these data used along with ancillary data as the fixed effects for RK of the new soil measurements.

An asymptotic preserving scheme for the vlasov-poisson-fokker-planck system in the high field regime

The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects (electrical or gravitational) are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field. We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime, namely, large time steps and coarse meshes can be used, yet the high field limit is still captured. The idea is to combine the two stiff terms and treat them implicitly. Thanks to the linearity of the collision term, using the discretization described in [Jin S, Yan B. J. Comp. Phys., 2011, 230: 6420–6437] we only need to invert a symmetric matrix. This method can be easily extended to higher dimensions. The method is shown to be positive, stable, mass and asymptotic preserving. Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes.

Meshless Helmholtz-Hodge Decomposition

Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements. This work presents a new meshless approach to the Helmholtz-Hodge decomposition for the analysis of 2D discrete vector fields. It embeds into the SPH particle-based framework. The proposed method is efficient and can be applied to extract features from a 2D discrete vector field and to multiphase fluid flow simulation to ensure incompressibility.

Modelling and mapping agricultural opportunity costs to guide landscape planning for natural resource management

On-farm actions to better manage natural resources often involve an opportunity cost associated with foregone agricultural production. Spatial information on agricultural opportunity costs is a key indicator that has been demonstrated to increase the cost-effectiveness of environmental investment through spatial targeting. In this paper we develop a method for calculating expected profit as a more robust spatial measure of economic rent accruing from agricultural land and indicator of opportunity cost for use in landscape and planning for natural resource management. We apply this method to the Lower Murray region in southern Australia. Agricultural profit is calculated for three farming system phases (cereals, legumes, and grazing) by census zones based on agricultural statistics and cost of production information within a GIS environment. Zonal profit layers are smoothed using pycnophylactic (mass preserving) interpolation. Farming system rotations are quantified as a set of continuous spatial probability layers for each phase using a moving window kernel density technique based on existing land use data and these probability layers are used in a weighted allocation of expected profit across the landscape. The expected profit layer provides a high spatial resolution description of opportunity costs associated with natural resource management over the Lower Murray region suitable for input into systematic landscape planning analyses. Validation of the opportunity cost layer by field survey identified both random and systematic error. Interpretation of systematic error highlighted the need to augment pycnophylactic interpolation techniques with consideration of covariates of profit such as rainfall for better estimation in areas with high profit gradients.

Fully conservative coupling of HEC-RAS with MODFLOW to simulate stream–aquifer interactions in a drainage basin

This work describes the application of a methodology designed to improve the representation of water surface profiles along open drain channels within the framework of regional groundwater modelling. The proposed methodology employs an iterative procedure that combines two public domain computational codes, MODFLOW and HEC-RAS. In spite of its known versatility, MODFLOW contains several limitations to reproduce elevation profiles of the free surface along open drain channels. The Drain Module available within MODFLOW simulates groundwater flow to open drain channels as a linear function of the difference between the hydraulic head in the aquifer and the hydraulic head in the drain, where it considers a static representation of water surface profiles along drains. The proposed methodology developed herein uses HEC-RAS, a one-dimensional (1D) computer code for open surface water calculations, to iteratively estimate hydraulic profiles along drain channels in order to improve the aquifer/drain interaction process. The approach is first validated with a simple closed analytical solution where it is shown that a Piccard iteration is enough to produce a numerically convergent and mass preserving solution. The methodology is then applied to the groundwater/surface water system of the Choele Choel Island, in the Patagonian region of Argentina. Smooth and realistic hydraulic profiles along drains are obtained while backwater effects are clearly represented.

SUSY structures on deformed supermanifolds

We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result is a representation of the supersymmetry algebra. In the case that the structure is mass preserving we describe all high energy corrections to this algebra.

Lattice-Boltzmann simulations in reconstructed parametrized porous media

Computations of flows in explicitly resolved porous media reported in the literature so far are based on binarized porous media data mapped to uniform Cartesian grids. The voxel set is directly being used as the computational grid and thus the geometrical representation is usually only first-order accurate due to stair-case patterns. In this work, we pursue a more elaborate approach: starting from a highly resolved tomographic grey value data set we utilize a Marching Cube algorithm to reconstruct the surface of the porous medium as a set of planar triangles. The numerical resolution of the Cartesian grid for the simulation can then be chosen independently from the voxel set. As we take into account the subgrid distances between the nodes of the Cartesian grid and the planar triangle surfaces, one can utilize a second-order accurate lattice Boltzmann flow solver to efficiently compute, e.g. permeabilities. As these interpolation-based no-slip boundary conditions are not mass preserving, we also present a local modification of the no-slip boundary condition restoring mass conservation. Our numerical results demonstrate that for saturated flow simulations this coupled approach allows a substantial acceleration of saturated flow computations in porous media.

Fully coupled “online” chemistry within the WRF model

A fully coupled “online” Weather Research and Forecasting/Chemistry (WRF/Chem) model has been developed. The air quality component of the model is fully consistent with the meteorological component; both components use the same transport scheme (mass and scalar preserving), the same grid (horizontal and vertical components), and the same physics schemes for subgrid-scale transport. The components also use the same timestep, hence no temporal interpolation is needed. The chemistry package consists of dry deposition (“flux-resistance” method), biogenic emission as in [Simpson et al., 1995. Journal of Geophysical Research 100D, 22875–22890; Guenther et al., 1994. Atmospheric Environment 28, 1197–1210], the chemical mechanism from RADM2, a complex photolysis scheme (Madronich scheme coupled with hydrometeors), and a state of the art aerosol module (MADE/SORGAM aerosol parameterization). The WRF/Chem model is statistically evaluated and compared to MM5/Chem and to detailed photochemical data collected during the summer 2002 NEAQS field study. It is shown that the WRF/Chem model is statistically better skilled in forecasting O 3 than MM5/Chem, with no appreciable differences between models in terms of bias with the observations. Furthermore, the WRF/Chem model consistently exhibits better skill at forecasting the O 3 precursors CO and NO y at all of the surface sites. However, the WRF/Chem model biases of these precursors and of other gas-phase species are persistently higher than for MM5/Chem, and are most often biased high compared to observations. Finally, we show that the impact of other basic model assumptions on these same statistics can be much larger than the differences caused by model differences. An example showing the sensitivity of various statistical measures with respect to the treatment of biogenic volatile organic compounds emissions illustrates this impact.

Fast calculation of energy and mass preserving solutions of Schrödinger–Poisson systems on unbounded domains

This paper deals with the numerical solution of the time-dependent Schrödinger–Poisson system in the spherically symmetric case. Since the problem is posed on an unbounded domain one has to introduce artificial boundary conditions to confine the computational domain. The main topic of this work is the construction of a so-called discrete transparent boundary condition (TBC) for a Crank–Nicolson-type predictor–corrector scheme for solving the Schrödinger–Poisson system. This scheme has the property of mass and energy conservation exactly on the discrete level. We propose different strategies for the discrete TBC and present an efficient implementation. Finally, a numerical example illustrate the findings and shows the comparison results between the different approaches.

Quantum Dynamical Semigroups for Diffusion Models with Hartree Interaction

We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global-in-time, mass preserving solutions is proved, thus establishing the existence of a nonlinear conservative quantum dynamical semigroup. The mathematical difficulties stem from combining an unbounded Lindblad generator with the Hartree nonlinearity.

On Fast-Diffusion Equations with Infinite Equilibrium Entropy and Finite Equilibrium Mass

We extend the existing theory on large-time asymptotics for convection–diffusion equations, based on the entropy–entropy dissipation approach, to certain fast diffusion equations with uniformly convex confinement potential and finite-mass but infinite-entropy equilibrium solutions. We prove existence of a mass preserving solution of the Cauchy problem and we show exponential convergence, as , at a precise rate to the corresponding equilibrium solution in the L 1 norm. As by-product we also derive corresponding generalized Sobolev inequalities.

Moving boundary problems and non-uniqueness for the thin film equation

A variety of mass preserving moving boundary problems for the thin film equation, ut = −(unuxxx)x, are derived (by formal asymptotics) from a number of regularisations, the case in which the substrate is covered by a very thin pre-wetting film being discussed in most detail. Some of the properties of the solutions selected in this fashion are described, and the full range of possible mass preserving non-negative solutions is outlined.

The dynamics of isocirculational flows

Abstract Barotropic flows are described in terms of mass preserving velocity fields of the vortex lines and non-barotropic flows by mass preserving velocity fields that move with the entropy and the potential vorticity. In these representations, all locally conserved quantities of inviscid flows are a priori given functions of the positions of the elements of fluid. The Hamiltonian action for these “isocirculational” flows is also given and is suitable for studying motions around given steady states. Stability conditions of stationary flows with respect to perturbations that are not necessarily small but that do not change the values of the conserved quantities including the circulations are obtained by minimizing the potential terms of the Lagrangian functional.