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Mitochondria and plastids rely on many nuclear-encoded genes, but retain small subsets of the genes they need to function in their own organelle DNA (oDNA). Different species retain different numbers of oDNA genes, and the reasons for these differences are not completely understood. Here, we use a mathematical model to explore the hypothesis that the energetic demands imposed by an organism's changing environment influence how many oDNA genes it retains. The model couples the physical biology of cell processes of gene expression and transport to a supply-and-demand model for the environmental dynamics to which an organism is exposed. The trade-off between fulfilling metabolic and bioenergetic environmental demands, and retaining genetic integrity, is quantified for a generic gene encoded either in oDNA or in nuclear DNA. Species in environments with high-amplitude, intermediate-frequency oscillations are predicted to retain the most organelle genes, whereas those in less dynamic or noisy environments the fewest. We discuss support for, and insight from, these predictions with oDNA data across eukaryotic taxa, including high oDNA gene counts in sessile organisms exposed to day-night and intertidal oscillations (including plants and algae) and low counts in parasites and fungi. [ABSTRACT FROM AUTHOR]

Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our formulation is novel in that it employs the normal fluxes as the mortar variable within the mixed finite element framework, resulting in a formulation that couples the flow in the fractures with the surrounding domain with a strong notion of mass conservation. The proposed discretization handles complex, nonmatching grids and allows for fracture intersections and termination in a natural way, as well as spatially varying apertures. The discretization is applicable to both two and three spatial dimensions. A priori analysis shows the method to be optimally convergent with respect to the chosen mixed finite element spaces, which is supported by numerical examples. [ABSTRACT FROM AUTHOR]

In this contribution, we develop a theoretical framework for linking microprocesses (i.e., population dynamics and evolution through natural selection) with macrophenomena (such as interconnectedness and modularity within an ecological system). This is achieved by developing a measure of interconnectedness for population distributions defined on a trait space (generalizing the notion of modularity on graphs), in combination with an evolution equation for the population distribution. With this contribution, we provide a platform for understanding under what environmental, ecological, and evolutionary conditions ecosystems evolve toward being more or less modular. A major contribution of this work is that we are able to decompose the overall driver of changes at the macro level (such as interconnectedness) into three components: (i) ecologically driven change, (ii) evolutionarily driven change, and (iii) environmentally driven change. [ABSTRACT FROM AUTHOR]

In geological storage of carbon dioxide (CO2), the buoyant CO2 plume eventually accumulates under the caprock. Due to interfacial tension between the CO2 phase and the water phase, a capillary transition zone develops in the plume. This zone contains supercritical CO2 as well as water with dissolved CO2. Under the plume, a diffusive boundary layer forms. We study how cross-flow between the capillary transition zone and the diffusive boundary layer affects gravitational stability of the diffusive boundary layer. Linear stability analysis shows that this cross-flow has no significant effect on the selection of the critical mode. However, interaction with the capillary transition zone enhances the instability of the boundary layer, such that the onset of instabilities occurs earlier, when the diffusive boundary layer is thinner. The onset time may be reduced by a factor of five, which corresponds to the thickness of the diffusive boundary layer at onset being reduced by a factor of two. This reduced thickness of the boundary layer at onset can be interpreted in terms of a reduced portion of the critical mode that must ’fit’ inside the boundary layer when the other portion of the mode is confined within the capillary transition zone. Direct numerical simulations for the non-linear regime show that the mass transfer rate can be enhanced up to four times when the cross-flow is accounted for. This increase is related to advective inflow of CO2-saturated water across the interface. Therefore, the contribution from dissolution to the safety of geological storage of CO2 begins earlier and can be considerably larger than showed by estimates that neglect the capillary transition zone. [ABSTRACT FROM AUTHOR]

For multi-phase flow in porous media, the fluids will experience reduced conductivity due to fluid-fluid interactions. This effect is modeled by the so-called relative permeability. The relative permeability is commonly assumed to be a scalar quantity, even though justifications for this modeling choice seldom are presented. In this paper, we show that the relative permeability can yield preferential flow directions, and that furthermore, these directions may vary as a function of the fluids present. To model these effects properly, the relative permeability should be considered a tensor. As shown in the paper, standard numerical methods cannot simulate tensor relative permeabilities. We therefore propose two new methods to remedy the situation. One scheme can be seen as an attempt to amend traditional methods to handle tensor relative permeabilities. The second scheme is a consistent approach to simulate the tensors. We also present numerical simulations of cases where upscaling leads to tensor relative permeabilities. The results show that the new methods are indeed capable of capturing tensor effects, moreover, they are in very good agreement with fine scale reference solutions. [ABSTRACT FROM AUTHOR]

The relentless increase of anthropogenic carbon dioxide emissions and the associated concerns about climate change have motivated new ideas about carbon-constrained energy production. One technological approach to control carbon dioxide emissions is carbon capture and storage, or CCS. The underlying idea of CCS is to capture the carbon before it emitted to the atmosphere and store it somewhere other than the atmosphere. Currently, the most attractive option for large-scale storage is in deep geological formations, including deep saline aquifers. Many physical and chemical processes can affect the fate of the injected CO2, with the overall mathematical description of the complete system becoming very complex. Our approach to the problem has been to reduce complexity as much as possible, so that we can focus on the few truly important questions about the injected CO2, most of which involve leakage out of the injection formation. Toward this end, we have established a set of simplifying assumptions that allow us to derive simplified models, which can be solved numerically or, for the most simplified cases, analytically. These simplified models allow calculation of solutions to large-scale injection and leakage problems in ways that traditional multicomponent multiphase simulators cannot. Such simplified models provide important tools for system analysis, screening calculations, and overall risk-assessment calculations. We believe this is a practical and important approach to model geological storage of carbon dioxide. It also serves as an example of how complex systems can be simplified while retaining the essential physics of the problem. [ABSTRACT FROM AUTHOR]

Geological storage of carbon dioxide (CO2) is likely to be an integral component of any realistic plan to reduce anthropogenic greenhouse gas emissions. In conjunction with large-scale deployment of carbon storage as a technology, there is an urgent need for tools which provide reliable and quick assessments of aquifer storage performance. Previously, abandoned wells from over a century of oil and gas exploration and production have been identified as critical potential leakage paths. The practical importance of abandoned wells is emphasized by the correlation of heavy CO2 emitters (typically associated with industrialized areas) to oil and gas producing regions in North America. Herein, we describe a novel framework for predicting the leakage from large numbers of abandoned wells, forming leakage paths connecting multiple subsurface permeable formations. The framework is designed to exploit analytical solutions to various components of the problem and, ultimately, leads to a grid-free approximation to CO2 and brine leakage rates, as well as fluid distributions. We apply our model in a comparison to an established numerical solver for the underlying governing equations. Thereafter, we demonstrate the capabilities of the model on typical field data taken from the vicinity of Edmonton, Alberta. This data set consists of over 500 wells and 1 permeable formations. Results show the flexibility and utility of the solution methods, and highlight the role that analytical and semianalytical solutions can play in this important problem. [ABSTRACT FROM AUTHOR]

Porous media are characterized by strongly heterogeneous properties on all scales of observation. This has motivated a sustained research effort in upscaling methods and lately multiscale methods. However, due to the lack of scale separation for realistic problems, static upscaling and multiscale methods may not be suitable in general, and adaptive approaches are needed. In this paper, we outline the application of an adaptive variational multiscale method for two-phase flow in porous media. We give the symmetric and nonsymmetric forms of the mixed variational multiscale method and suggest a framework for adaptively selecting the support of the fine scale Green's operators in space and time. The applicability of our framework is validated through a set of numerical comparisons. [ABSTRACT FROM AUTHOR]

Abstract: We study the dynamics of soil moisture in the presence of precipitation, evapotranspiration and leakage. This study utilizes a probabilistic framework, and considers the evolution of the probability density function of soil moisture. Our main objective is to assess when the stationary solution is a physically realizable state of the system. Mathematically, this is equivalent to analyzing when the stationary solutions are stable. We show the following main results: For a general rainfall and evapotranspiration model, in a multiple plant framework, the stationary solution is a stable attractor in L 1. However, the stationary solution is at best conditionally stable in L ∞. This has important implications in terms of (1) the validity of moment analysis of the transient problem, (2) the physical importance of transient solutions, and (3) the numerical solution of the stationary problem as a late time solution of the transient problem. [Copyright &y& Elsevier]

This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary modeling and simulation tools. Care is also taken to establish a solid mathematical foundation on which our modeling framework is built. This is the subject of the first half of the paper. The second half is devoted to developing a multiscale framework for eco-evolutionary modeling, where the relevant scales are that of species and individual/population, respectively. The species level model we employ can be considered as an extension of the classical Lotka--Volterra model, where in addition to the species abundance, the model also governs the evolution of the species mean traits and species trait covariances and in this sense generalizes the purely ecological Lotka--Volterra model to an eco-evolutionary model. Although the model thus allows for evolving species, it does not (by construction) allow for the branching of species, i.e., speciation events. The reason for this is related to that of separate scales; the unit of species is too coarse to capture the fine-scale dynamics of a speciation event. Instead, the branching species should be regarded as a population of individuals moving along a selection of trait axes (i.e., trait-space). For this, we employ a trait-specific population density model governing the dynamics of the population density as a function of evolutionary traits. At this scale there is no a priori definition of species, but both species and speciation may be defined a posteriori as, e.g., local maxima and saddle points of the population density, respectively. Hence, a system of interacting species can be described at the species level, while for branching species a population level description is necessary. Our multiscale framework thus consists of coupling the species and population level models where speciation events are detected in advance and then resolved at the population scale until the branching is complete. Moreover, since the population level model is formulated as a PDE, we first establish the well-posedness in the time-discrete setting and then derive the a posteriori error estimates, which provides a fully computable upper bound on an energy-type error, including also for the case of general smooth distributions (which will be useful for the detection of speciation events). Several numerical tests validate our framework in practice. [ABSTRACT FROM AUTHOR]

Abstract: Control volume methods are prevailing for solving the potential equation arising in porous media flow. The continuous form of this equation is known to satisfy a maximum principle, and it is desirable that the numerical approximation shares this quality. Recently, sufficient criteria were derived guaranteeing a discrete maximum principle for a class of control volume methods. We show that most of these criteria are also necessary. An implication of our work is that no linear nine-point control volume method can be constructed for quadrilateral grids in 2D that is exact for linear solutions while remaining monotone for general problems. [Copyright &y& Elsevier]

In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becoming popular in applications, in particular, to model the human vasculature. We first discuss the model equations in the strong form which describes the conservation of mass and Darcy's law in the continuum and network as well as the coupling between them. By introducing proper scaling, we propose a weak form that avoids degeneracy. Well-posedness of the weak form is shown through standard Babuška-Brezzi theory. We also develop the mixed formulation finite-element method and prove its well-posedness. A mass-lumping technique is introduced to derive the two-point flux approximation type discretization as well, due to its importance in applications. Based on the Babuška-Brezzi theory, error estimates can be obtained for both the finite-element scheme and the TPFA scheme. We also discuss efficient linear solvers for discrete problems. Finally, we present some numerical examples to verify the theoretical results and demonstrate the robustness of our proposed discretization schemes. [ABSTRACT FROM AUTHOR]

In this work we consider the dual-mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is nonstandard, as the line source causes the solutions to be singular. We start by showing that this problem admits a solution in appropriately weighted Sobolev spaces. Next, we show that given some assumptions on the problem parameters, the solution admits a splitting into higher- and lower-regularity terms. The lower-regularity terms are here explicitly known and capture the solution singularities. The higher-regularity terms, meanwhile, are defined as the solution of an associated mixed Poisson equation. With the solution splitting in hand, we then define a singularity removal--based mixed finite element method in which only the higher-regularity terms are approximated numerically. This method yields a significant improvement in the convergence rate when compared to approximating the full solution. In particular, we show that the singularity removal--based method yields optimal convergence rates for lowest-order Raviart--Thomas and discontinuous Lagrange elements. [ABSTRACT FROM AUTHOR]

Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory of functional a posteriori error estimates, for which guaranteed upper bounds for the primal and dual variables and two-sided bounds for the primal–dual pair are obtained. We improve on the abstract results obtained with the functional approach by proposing four different ways of estimating the residual errors based on the extent the approximate solution has conservation properties, i.e., (1) no conservation, (2) subdomain conservation, (3) grid-level conservation, and (4) exact conservation. This treatment results in sharper and fully computable estimates when mass is conserved either at the grid level or exactly, with a comparable structure to those obtained from grid-based a posteriori techniques. We demonstrate the practical effectiveness of our theoretical results through numerical experiments using four different discretization methods for synthetic problems and applications based on benchmarks of flow in fractured porous media. [ABSTRACT FROM AUTHOR]

In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this work, we consider a coupled 1D–3D flow model, in which the well is modelled as a line source in the reservoir domain and endowed with its own 1D flow equation. The flow between well and reservoir can then be modelled in a fully coupled manner by applying a linear filtration law. The line source induces a logarithmic-type singularity in the reservoir pressure that is difficult to resolve numerically. We present here a singularity removal method for the model equations, resulting in a reformulated coupled 1D–3D flow model in which all variables are smooth. The singularity removal is based on a solution splitting of the reservoir pressure, where it is decomposed into two terms: an explicitly given, lower-regularity term capturing the solution singularity and some smooth background pressure. The singularities can then be removed from the system by subtracting them from the governing equations. Finally, the coupled 1D–3D flow equations can be reformulated so they are given in terms of the well pressure and the background reservoir pressure. As these variables are both smooth (i.e. non-singular), the reformulated model has the advantage that it can be approximated using any standard numerical method. The reformulation itself resembles a Peaceman well correction performed at the continuous level. [ABSTRACT FROM AUTHOR]

We develop a new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids. Motivated by the multipoint flux mixed finite element method for Darcy flow, the method utilizes the lowest order Brezzi--Douglas--Marini finite element spaces for the stress and the vertex quadrature rule in order to localize the interaction of degrees of freedom. This allows for local stress elimination around each vertex. We develop two variants of the method. The first uses a piecewise constant rotation and results in a cell-centered system for displacement and rotation. The second uses a piecewise linear rotation and a quadrature rule for the asymmetry bilinear form. This allows for further elimination of the rotation, resulting in a cell-centered system for the displacement only. Stability and error analysis is performed for both variants. First order convergence is established for all variables in their natural norms. A duality argument is further employed to prove second order superconvergence of the displacement at the cell centers. Numerical results are presented in confirmation of the theory. [ABSTRACT FROM AUTHOR]

Upscaling of flow from pore to Darcy scale is a long-standing research field within flow in porous media. It is well known that non-linearities can occur in near-well regions and high-porosity or fractured media. At the same time, the upscaled non-linear effects associated with high flow rates are hard to quantify a priori with single-scale models. Advances in pore-scale imaging combined with increased computational have made flow simulations in small pore-scale domain feasible, but computations on domains larger than at most a few centimeters are still elusive. In this work, we present a multiscale simulation framework that automatically adapts to non-linear effects as they arise. We formulate a control volume heterogeneous multiscale method (CVHMM) by coupling of a Darcy-scale control volume method with a constitutive relation that is captured based on the fine-scale physics. While the CVHMM formulation works with arbitrary upscaled laws, we emphasize its ability to be applied in fully discrete multiscale context, in particular when a finite element solver is used for solving Navier-Stokes equations on the fine-scale pore geometry. Previous versions of CVHMM are consistent only when the coarse grid is aligned with the upscaled permeability. Herein, we generalize CVHMM by introducing a new coarse solver, thus significantly improving the applicability of the method. The presented method is applied to study flow in near-well regions, as well as media with fractures and irregular grain shapes. The examples show that the method successfully copes with general grids and pore geometries and handles flows with varying degree of non-linearities even outside the domain of applicability of classical upscaled models. In terms of computational efficiency, the method seamlessly localizes computations to regions where non-linear effects are important. [ABSTRACT FROM AUTHOR]

In this work, we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists of two fully coupled, nonlinear equations: a degenerate parabolic equation and an elliptic one. The proposed numerical scheme is based on backward Euler for the temporal discretization and mixed finite element method for the spatial one. A priori stability and error estimates are presented to prove the convergence of the scheme. A monotone increasing, Höolder continuous saturation is considered. The convergence of the scheme is naturally dependant on the Hölder exponent. The nonlinear systems within each time step are solved by a robust linearization method, called the L-scheme. This iterative method does not involve any regularization step. The convergence of the L-scheme is rigorously proved under the assumption of a Lipschitz continuous saturation. For the Höolder continuous case, a numerical convergence is established. Numerical results (two-dimensional and three-dimensional) are presented to sustain the theoretical findings. [ABSTRACT FROM AUTHOR]

It is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct non-monotone solutions of the Buckley–Leverett equation. These solutions are interpreted using a recent variational definition of delta shock waves in which the Rankine–Hugoniot deficit is explicitly accounted for [6] . The delta shock waves are also limits of approximate solutions constructed using a recent extension of the weak asymptotic method to complex-valued approximations [15] . Finally, it is shown how these non-standard shocks can be fitted together to construct similarity and traveling-wave solutions which are non-monotone, but still admissible in the sense that characteristics either enter or are parallel to the shock trajectories. [ABSTRACT FROM AUTHOR]

Abstract: The multiscale control-volume methods for solving problems involving flow in porous media have gained much interest during the last decade. Recasting these methods in an algebraic framework allows one to consider them as preconditioners for iterative solvers. Despite intense research on the 2D formulation, few results have been shown for 3D, where indeed the performance of multiscale methods deteriorates. The interpretation of multiscale methods as vertex based domain decomposition methods, which are non-scalable for 3D domain decomposition problems, allows us to understand this loss of performance. We propose a generalized framework based on auxiliary variables on the coarse scale. These are enrichments of the coarse scale, which can be selected to improve the interpolation onto the fine scale. Where the existing coarse scale basis functions are designed to capture local sub-scale heterogeneities, the auxiliary variables are aimed at better capturing non-local effects resulting from non-linear behavior of the pressure field. The auxiliary coarse nodes fits into the framework of mass-conservative domain-decomposition (MCDD) preconditioners, allowing us to construct, as special cases, both the traditional (vertex based) multiscale methods as well as their wire basket generalization. [Copyright &y& Elsevier]

Abstract: Domain decomposition (DD) methods, such as the additive Schwarz method, are almost exclusively applied to linearized equations. In the context of nonlinear problems, these linear systems appear as part of a Newton iteration. However, applying DD methods directly to the original nonlinear problem has some attractive features, most notably that the Newton iterations now solve local problems, and thus are expected to be simpler. Furthermore, strong, local nonlinearities may to a less extent affect the numerical algorithm. For linear problems, DD can be applied both as an iterative solver or as a preconditioner. For nonlinear problems, it has until recently only been understood how to use DD as a solver. This article offers a systematic study of domain decomposition strategies in the context of nonlinear porous-medium flow problems. The study thus compares four different approaches, which represents DD applied both as a solver and preconditioner, to both the linearized and nonlinear equations. Our model equations are those obtained from a fully implicit discretization of immiscible two-phase flow in heterogeneous porous media. In particular we emphasize the case of nonlinear preconditioning, an algorithm that to our knowledge so far has not been studied nor implemented for flow in porous media. Our results show that the novel algorithm is up to 75% faster than the standard algorithm for the most challenging problems for a moderate number of subdomains. [Copyright &y& Elsevier]

We uncover novel features of three-dimensional natural convection in porous media by investigating convection in an annular porous cavity contained between two vertical coaxial cylinders. The investigations are made using a linear stability analysis, together with high-order numerical simulations using pseudospectral methods to model the nonlinear regime. The onset of convection cells and their preferred planform are studied, and the stability of the modes with respect to different types of perturbation is investigated. We also examine how variations in the Rayleigh number affect the convection modes and their stability regimes. Compared with previously published data, we show how the problem inherits an increased complexity regarding which modes will be obtained. Some stable secondary modes or mixed modes have been identified and some overlapping stability regions for different convective modes are determined. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a quantitative ecohydrological framework for predicting regional distribution patterns of woody species in dryland ecosystems. The framework is based on an existing stochastic model for the daily mass balance of water that represents the interactions between soils, climate, and vegetation. Individual species selection is based on an optimality trade-off hypothesis, which states that dryland vegetation patterns are constrained by maximization of water use and simultaneous minimization of water stress. The relative importance of water use and stress avoidance to the overall fitness of three Acacia species is determined from the heterogeneous basin, the Upper Ewaso Ng’iro river basin, of the central Kenya highlands. The model results indicate that overall fitness is more strongly influenced by water use than stress avoidance but that consideration of both stress avoidance and water use is critical to predicting basin-scale patterns of species distribution. We identify a linear trend in the frequency and intensity of storms with the same annual total using a basin-wide gauge precipitation dataset. After calibration, we apply the basin average linear trends in time for average rain per storm and storm arrival rates. The model results indicate the upslope migration of two species, Acacia tortilis and Acacia xanthophloea to areas with higher total rainfall. Lastly, we explore the modeled changes of species cover in the basin influenced by changes in rainfall total holding growing season rainfall variability constant and changes in growing season rainfall variability holding total rainfall constant. We find that changes in dryland species distribution patterns and relative abundance may be as sensitive to growing season rainfall variability as they are to changes in total rainfall amounts. [Copyright &y& Elsevier]

In this work, we consider compressible single-phase flow problems in a porous medium containing a fracture. In the fracture, a nonlinear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we reformulate the global problem into a nonlinear interface problem. We then introduce two new algorithms that are able to efficiently handle the nonlinearity and the coupling between the fracture and the matrix, both based on linearization by the so-called L-scheme. The first algorithm, named MoLDD, uses the L-scheme to resolve for the nonlinearity, requiring at each iteration to solve the dimensional coupling via a domain decomposition approach. The second algorithm, called ItLDD, uses a sequential approach in which the dimensional coupling is part of the linearization iterations. For both algorithms, the computations are reduced only to the fracture by precomputing, in an offline phase, a multiscale flux basis (the linear Robin-to-Neumann codimensional map), that represent the flux exchange between the fracture and the matrix. We present extensive theoretical findings X and in particular, t. The stability and the convergence of both schemes are obtained, where user-given parameters are optimized to minimize the number of iterations. Examples on two important fracture models are computed with the library PorePy and agree with the developed theory. [ABSTRACT FROM AUTHOR]

A large variety of severe medical conditions involve alterations in microvascular circulation. Hence, measurements or simulation of circulation and perfusion has considerable clinical value and can be used for diagnostics, evaluation of treatment efficacy, and for surgical planning. However, the accuracy of traditional tracer kinetic one-compartment models is limited due to scale dependency. As a remedy, we propose a scale invariant mathematical framework for simulating whole brain perfusion. The suggested framework is based on a segmentation of anatomical geometry down to imaging voxel resolution. Large vessels in the arterial and venous network are identified from time-of-flight (ToF) and quantitative susceptibility mapping (QSM). Macro-scale flow in the large-vessel-network is accurately modelled using the Hagen-Poiseuille equation, whereas capillary flow is treated as two-compartment porous media flow. Macro-scale flow is coupled with micro-scale flow by a spatially distributing support function in the terminal endings. Perfusion is defined as the transition of fluid from the arterial to the venous compartment. We demonstrate a whole brain simulation of tracer propagation on a realistic geometric model of the human brain, where the model comprises distinct areas of grey and white matter, as well as large vessels in the arterial and venous vascular network. Our proposed framework is an accurate and viable alternative to traditional compartment models, with high relevance for simulation of brain perfusion and also for restoration of field parameters in clinical brain perfusion applications. [ABSTRACT FROM AUTHOR]

Objective: Chronic kidney disease (CKD) is a serious medical condition characterized by gradual loss of kidney function. Early detection and diagnosis is mandatory for adequate therapy and prognostic improvement. Hence, in the current pilot study we explore the use of image registration methods for detecting renal morphologic changes in patients with CKD. Methods: Ten healthy volunteers and nine patients with presumed CKD underwent dynamic T1 weighted imaging without contrast agent. From real and simulated dynamic time series, kidney deformation fields were estimated using a poroelastic deformation model. From the deformation fields several quantitative parameters reflecting pressure gradients, and volumetric and shear deformations were computed. Eight of the patients also underwent a kidney biopsy as a gold standard. Results: We found that the absolute deformation, normalized volume changes, as well as pressure gradients correlated significantly with arteriosclerosis from biopsy assessments. Furthermore, our results indicate that current image registration methodologies are lacking sensitivity to recover mild changes in tissue stiffness. Conclusion: Image registration applied to dynamic time series correlated with structural renal changes and should be further explored as a tool for invasive measurements of arteriosclerosis. Significance: Under the assumption that the proposed framework can be further developed in terms of sensitivity and specificity, it can provide clinicians with a non-invasive tool of high spatial coverage available for characterization of arteriosclerosis and potentially other pathological changes observed in chronic kidney disease. [ABSTRACT FROM AUTHOR]

We consider a non-linear extension of Biot’s model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. Specifically, we study the case when the volumetric stress and the fluid density are non-linear functions satisfying certain assumptions. We perform an implicit discretization in time (backward Euler) and propose two iterative schemes for solving the non-linear problems appearing within each time step: a splitting algorithm extending the undrained split and fixed stress methods to non-linear problems, and a monolithic L-scheme. The convergence of both schemes are shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results. [ABSTRACT FROM AUTHOR]

Groundwater discharge to streams depends on stream morphology and groundwater flow direction, but are not always well understood. Here a 3-D groundwater flow model is employed to investigate the impact of meandering stream geometries on groundwater discharge to streams in an unconfined and homogenous sandy aquifer at the reach scale (10–200 m). The effect of meander geometry was examined by considering three scenarios with varying stream sinuosity. The interaction with regional groundwater flow was examined for each scenario by considering three groundwater flow directions. The sensitivity of stream morphology and flow direction to other parameters was quantified by varying the stream width, the meander amplitude, the magnitude of the hydraulic gradient, the hydraulic conductivity, and the aquifer thickness. Implications for a real stream were then investigated by simulating groundwater flow to a stream at a field site located in Grindsted, Denmark. The simulation of multiple scenarios was made possible by the employment of a computationally efficient coordinate transform numerical method. Comparison of the scenarios showed that the geometry of meanders greatly affect the spatial distribution of groundwater flow to streams. The shallow part of the aquifer discharges to the outward pointing meanders, while deeper groundwater flows beneath the stream and enters from the opposite side. The balance between these two types of flow depends on the aquifer thickness and meander geometry. Regional groundwater flow can combine with the effect of stream meanders and can either enhance or smooth the effect of a meander bend, depending on the regional flow direction. Results from the Grindsted site model showed that real meander geometries had similar effects to those observed for the simpler sinuous streams, and showed that despite large temporal variations in stream discharge, the spatial pattern of flow is almost constant in time for a gaining stream. [ABSTRACT FROM AUTHOR]

Objective: Medical image registration can be formulated as a tissue deformation problem, where parameter estimation methods are used to obtain the inverse deformation. However, there is limited knowledge about the ability to recover an unknown deformation. The main objective of this study is to estimate the quality of a restored deformation field obtained from image registration of dynamic MR sequences. Methods: We investigate the behavior of forward deformation models of various complexities. Further, we study the accuracy of restored inverse deformations generated by image registration. Results: We found that the choice of 1) heterogeneous tissue parameters and 2) a poroelastic (instead of elastic) model had significant impact on the forward deformation. In the image registration problem, both 1) and 2) were found not to be significant. Here, the presence of image features were dominating the performance. We also found that existing algorithms will align images with high precision while at the same time obtain a deformation field with a relative error of $40\%$. Conclusion: Image registration can only moderately well restore the true deformation field. Still, estimation of volume changes instead of deformation fields can be fairly accurate and may represent a proxy for variations in tissue characteristics. Volume changes remain essentially unchanged under choice of discretization and the prevalence of pronounced image features. Significance: We suggest that image registration of high-contrast MR images has potential to be used as a tool to produce imaging biomarkers sensitive to pathology affecting tissue stiffness. [ABSTRACT FROM PUBLISHER]