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Merosin deficient congenital muscular dystrophy 1A (MDC1A) is a very rare autosomal recessive disorder caused by mutations in the LAMA2 gene leading to severe and progressive muscle weakness and atrophy. Although over 350 causative mutations have been identified for MDC1A, no treatment is yet available. There are many therapeutic approaches in development, but the lack of natural history data of the mouse model and standardized outcome measures makes it difficult to transit these pre-clinical findings to clinical trials. Therefore, in the present study, we collected natural history data and assessed pre-clinical outcome measures for the dy2J/dy2J mouse model using standardized operating procedures available from the TREAT-NMD Alliance. Wild type and dy2J/dy2J mice were subjected to five different functional tests from the age of four to 32 weeks. Non-tested control groups were taken along to assess whether the functional test regime interfered with muscle pathology. Respiratory function, body weights and creatine kinase levels were recorded. Lastly, skeletal muscles were collected for further histopathological and gene expression analyses. Muscle function of dy2J/dy2J mice was severely impaired at four weeks of age and all mice lost the ability to use their hind limbs. Moreover, respiratory function was altered in dy2J/dy2J mice. Interestingly, the respiration rate was decreased and declined with age, whereas the respiration amplitude was increased in dy2J/dy2J mice when compared to wild type mice. Creatine kinase levels were comparable to wild type mice. Muscle histopathology and gene expression analysis revealed that there was a specific regional distribution pattern of muscle damage in dy2J/dy2J mice. Gastrocnemius appeared to be the most severely affected muscle with a high proportion of atrophic fibers, increased fibrosis and inflammation. By contrast, triceps was affected moderately and diaphragm only mildly. Our study presents a complete natural history dataset which can be used in setting up standardized studies in dy2J/dy2J mice. [ABSTRACT FROM AUTHOR]

Limb-girdle muscular dystrophy types 2D and 2F (LGMD 2D and 2F) are autosomal recessive disorders caused by mutations in the alpha- and delta sarcoglycan genes, respectively, leading to severe muscle weakness and degeneration. The cause of the disease has been well characterized and a number of animal models are available for pre-clinical studies to test potential therapeutic interventions. To facilitate transition from drug discovery to clinical trials, standardized procedures and natural disease history data were collected for these mouse models. Implementing the TREAD-NMD standardized operating procedures, we here subjected LGMD2D (SGCA-null), LGMD2F (SGCD-null) and wild type (C57BL/6J) mice to five functional tests from the age of 4 to 32 weeks. To assess whether the functional test regime interfered with disease pathology, sedentary groups were taken along. Muscle physiology testing of tibialis anterior muscle was performed at the age of 34 weeks. Muscle histopathology and gene expression was analysed in skeletal muscles and heart. Muscle histopathology and gene expression was analysed in skeletal muscles and heart. Mice successfully accomplished the functional tests, which did not interfere with disease pathology. Muscle function of SGCA- and SGCD-null mice was impaired and declined over time. Interestingly, female SGCD-null mice outperformed males in the two and four limb hanging tests, which proved the most suitable non-invasive tests to assess muscle function. Muscle physiology testing of tibialis anterior muscle revealed lower specific force and higher susceptibility to eccentric-induced damage in LGMD mice. Analyzing muscle histopathology and gene expression, we identified the diaphragm as the most affected muscle in LGMD strains. Cardiac fibrosis was found in SGCD-null mice, being more severe in males than in females. Our study offers a comprehensive natural history dataset which will be useful to design standardized tests and future pre-clinical studies in LGMD2D and 2F mice. [ABSTRACT FROM AUTHOR]

Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream-aquifer exchanges, and (H3) the biases result from slow paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream-aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW (Modular Three-dimensional Finite-difference Groundwater Flow Model) simulation environment, and the PEST (parameter estimation) tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop lognormally distributed conductivity (K) fields on local grid scales. Stream-aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce coherent slow paths in groundwater fluxes that in turn reduce aquifer-stream exchanges. Since surface water- groundwater exchanges are critical hydrologic processes in basin-scale water budgets, these results also have implications for water resources management. [ABSTRACT FROM AUTHOR]

We analyze scale-dependent statistics of correlated random hydrogeological variables and their extremes using neutron porosity data from six deep boreholes, in three diverse depositional environments, as example.We show that key statistics of porosity increments behave and scale in manners typical of many earth and environmental (as well as other) variables. These scaling behaviors include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over threshold or POTs. In this paper we explore the statistical scaling of data and, for the first time, corresponding POTs associated with samples from scale mixtures of tfBm or tfGn. We demonstrate that porosity data we analyze possess properties of such samples and thus follow the theory we proposed. The porosity data are of additional value in revealing a remarkable cross-over from one scaling regime to another at certain lags. The phenomena we uncover are of key importance for the analysis of fluid flow and solute as well as particulate transport in complex hydrogeologic environments. [ABSTRACT FROM AUTHOR]

In this paper we propose an analytical form for the upscaled coefficient applicable to the nonlinear Richards' equation. Block inclusions are symmetrically centered in a grid cell, and flow is dominated by capillary forces on the small scale. The nonlinear boundary value problems can be defined in a three-dimensional bounded domain, with a periodic and rapidly oscillating saturated hydraulic conductivity coefficient. The new result is derived by applying a corrector to an analytical approximation of the well-known cell problem obtained by the two-scale asymptotic expansion to the original heterogeneous nonlinear problem. The previously known analytical results for the upscaled coefficient, including the geometric average for the checkerboard geometry, can be regarded as particular cases of this new form. We perform numerical simulations to obtain the error between the fine-scale solution and the upscaled solution, respectively, as well as convergence properties of the approximation, corroborating results in the literature. There is no limitation regarding either the ratio of permeability between the matrix and inclusion or its shape for both computing the upscaled coefficient and obtaining the upscaled equation. This is illustrated by the comparison with known results and by numerically demonstrating convergence properties with a medium having square and circular inclusions in a main matrix with heterogeneity ratio of 1:100 and 1:10. Even though the derivation and applications are presented for single phase and steady state, the results are valid for multiphase and transient flow conditions. We also show that the approximation is independent of the relative saturated hydraulic relationship. [ABSTRACT FROM AUTHOR]

We present a model of reduced complexity for assessing the risk of groundwater pollution from a point source. The progress of contamination is represented as a sequence of transitions among coarsely resolved states corresponding to simple statements like 'a spill has occurred.' Transitions between states are modeled as a Markov jump process, and a general expression for the probability of aquifer contamination is obtained from two basic assumptions: that the sequence of transitions leading to contamination is Markovian and that the time when a given transition occurs is independent of its end state. Additionally, we derive an asymptotic value for the probability of contamination that is equivalent to the so-called rare event approximation. First we develop the model for sites in statistically homogeneous natural porous media, and then we extend it to highly heterogeneous media composed of multiple materials. Finally, we apply the model to a simple example to illustrate the method and its potential. [ABSTRACT FROM AUTHOR]

In this opinion paper we contend that high-resolution characterization, monitoring, and prediction are the key elements to advancing and reducing uncertainty in our understanding and prediction of subsurface processes at basin scales. First, we advocate that recently developed tomographic surveying is an effective and high-resolution approach for characterizing the field-scale subsurface. Fusion of different types of tomographic surveys further enhances the characterization. A basin is an appropriate scale for many water resources management purposes. We thereby propose the expansion of the tomographic surveying and data fusion concept to basin-scale characterization. In order to facilitate basin-scale tomographic surveys, different types of passive, basin-scale, CAT scan technologies are suggested that exploit recurrent natural stimuli (e.g., lightning, earthquakes, storm events, barometric variations, river-stage variations, etc.) as sources of excitations, along with implementation of sensor networks that provide long-term and spatially distributed monitoring of excitation as well as response signals on the land surface and in the subsurface. This vision for basin-scale subsurface characterization faces many significant technological challenges and requires interdisciplinary collaborations (e.g., surface and subsurface hydrology, geophysics, geology, geochemistry, information and sensor technology, applied mathematics, atmospheric science, etc.). We nevertheless contend that this should be a future direction for subsurface science research. [ABSTRACT FROM AUTHOR]

We introduce a stochastic model of flow through highly heterogeneous, composite porous media that greatly improves estimates of pressure head statistics. Composite porous media consist of disjoint blocks of permeable materials, each block comprising a single material type. Within a composite medium, hydraulic conductivity can be represented through a pair of random processes: (1) a boundary process that determines block arrangement and extent and (2) a stationary process that defines conductivity within a given block. We obtain second-order statistics for hydraulic conductivity in the composite model and then contrast them with statistics obtained from a standard univariate model that ignores the boundary process and treats a composite medium as if it were statistically homogeneous. Next, we develop perturbation expansions for the first two moments of head and contrast them with expansions based on the homogeneous approximation. In most cases the bivariate model leads to much sharper perturbation approximations than does the usual model of flow through an undifferentiated material when both are applied to highly heterogeneous media. We make this statement precise. We illustrate the composite model with examples of one-dimensional flows which are interesting in their own right and which allow us to compare the accuracy of perturbation approximations of head statistics to exact analytical solutions. We also show the boundary process of our bivariate model is equivalent to the indicator functions often used to represent composite media in Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

We analyze flow in heterogeneous media composed of multiple materials whose hydraulic properties and geometries are uncertain. Our analysis relies on the composite media theory of Winter and Tartakovsky [2000, 2002], which allows one to derive and solve moment equations even when the medium is highly heterogeneous. We use numerical solutions of Darcy flows through a representative composite medium to investigate the robustness of perturbation approximations in porous medium with total log conductivity variances as high as 20. We also investigate the relative importance of the two sources of uncertainty in composite media, material properties, and geometry. In our examples the uncertain geometry by itself captures the main features of the mean head estimated by the full composite model even when the within-material conductivities are deterministic. However, neglecting randomness within materials leads to head variance estimates that are qualitatively and quantitatively wrong. We compare the composite media approach to approximations that replace statistically inhomogeneous conductivity fields with pseudohomogeneous random fields with deterministic trends. We demonstrate that models with a deterministic trend can be expected to give a poor estimate of the statistics of head. [ABSTRACT FROM AUTHOR]

In this study we develop a first-order, nonstationary stochastic model for steady state, unsaturated flow in randomly heterogeneous media. The model is applicable to the entire domain of a bounded vadose zone, unlike most of the existing stochastic models. Because of its nonstationarity, we solve it by the numerical technique of finite differences, which renders the flexibility in handling different boundary conditions, input covariance structures, and soil constitutive relationships. We illustrate the model results in one and two dimensions for soils described by the Brooks-Corey constitutive model. It is found that the flow quantities such as suction head, effective water content, unsaturated hydraulic conductivity, and velocity are nonstationary near the water table and approach stationarity as the vertical distance from the water table increases. The stationary limits and the critical vertical distance at which stationarity is attained depend on soil types and recharge rates. The smaller the recharge rate is, the larger the critical distance; and the coarser the soil texture is, the smaller the distance. One important implication of this is that the existing simpler, gravity-dominated flow models may provide good approximations for flow in vadose zones of large thickness and/or coarse-textured soils although they may not be valid for vadose zones of fine-textured soils with a shallow water table. It is also found that the vertical extent of a domain where nonstationarity is important may be estimated by solving the one-dimensional Richards equation for mean head with average soil properties and appropriate boundary conditions. On the basis of the mean head, one may then determine whether the full, nonstationary model must be solved or whether a simpler, gavity-dominated model will suffice. The flow quantities are also nonstationary in the horizontal direction near the lateral boundaries, as found for flow in saturated zones. [ABSTRACT FROM AUTHOR]

Many of hydrogeology’s most fundamental questions remain unresolved today, a hundred years after the basic governing equations for groundwater flow and transport were formulated. This paper provides a brief overview of the field and outlines the future directions, with a special emphasis on uncertainty quantification. [ABSTRACT FROM AUTHOR]

We perform a set of detailed numerical simulations of single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (?) and degrees of connectivity, and analyze the probability density functions (PDFs) of the pore sizes, S, and vertical velocity components, w, which are aligned with the mean flow direction. Both of the PDFs are markedly skewed with pronounced positive tails. This feature of the velocity PDF is dictated by the pore structure and determines the shortest travel times, one of the key transport attributes that underpins the success or the failure of environmental remediation techniques. Using a maximum likelihood approach, we determine that the PDFs of S and w decay according to an exponential and a stretched exponential model, respectively. A strong correlation between the key parameters governing the decay of the upper tails of the two PDFs is found, which provides a quantitative result for this analogy that so far has been stated only qualitatively. The parameter governing the concavity of the tail of the velocity PDF varies linearly with porosity over the entire range of tested values (0.2=?=0.6). The parameters controlling the spread of the upper tails of the PDFs of S and w appear to be linked by a power-law relationship. [ABSTRACT FROM AUTHOR]