Stochastic Heterogeneity Research Articles

The Influence of Soil Stochastic Heterogeneity and Facility Dimensions on Stormwater Infiltration Facilities Performance

The progressive increase of impervious surfaces induced by urbanization altered significantly the natural hydrological cycle of urban catchments. To face the need of more sustainable and effective solutions for stormwater management and planning, Low Impact Development (LID) practices have been frequently proposed to support existing urban drainage systems. Among LID infrastructures, design and management of stormwater infiltration facilities are still characterised by a high degree of uncertainty. Since the stochastic heterogeneity of the soil may affect significantly their hydraulic performance, it is crucial to understand whether it should be accounted for in the design process. To this aim, numerical experiments under transient variably water saturated conditions were performed. Four infiltration facilities of different bottom length subjected to the same spatial variability of the intrinsic permeability field were considered. Simulations showed that the effects of stochastic heterogeneity on the hydraulic performance are dependent on the dimensions of the facility and on the correlation lengths of the intrinsic permeability field. These effects may potentially undermine the capacity to capture stormwater. To be reduced, the bottom dimensions of the facility should be higher than the horizontal correlation lengths of the intrinsic permeability field. Most strikingly, whether the stochastic heterogeneity is considered or not, the volume infiltrated through the bottom follows an increasing power law with increasing bottom length, while the average infiltration rate at the bottom follows a decaying power law.

Drywell infiltration and hydraulic properties in heterogeneous soil profiles

Drywells are increasingly used to capture stormwater runoff for surface infiltration and aquifer recharge, but little research has examined the role of ubiquitous subsurface heterogeneity in hydraulic properties on drywell performance. Numerical experiments were therefore conducted using the HYDRUS (2D/3D) software to systematically study the influence of subsurface heterogeneity on drywell infiltration. Subsurface heterogeneity was described deterministically by defining soil layers or lenses, or by generating stochastic realizations of soil hydraulic properties with selected variance (σ) and horizontal (X) and vertical (Z) correlation lengths. The infiltration rate increased when a high permeability layer/lens was located at the bottom of the drywell, and had larger vertical and especially horizontal dimensions. Furthermore, the average cumulative infiltration (I) for 100 stochastic realizations of a given subsurface heterogeneity increased with σ and X, but decreased with Z. This indicates that the presence of many highly permeable, laterally extending lenses provides a larger surface area for enhanced infiltration than the presence of isolated, highly permeable lenses. The ability to inversely determine soil hydraulic properties from numerical drywell infiltration results was also investigated. The hydraulic properties and the lateral extension of a highly permeable lens could be accurately determined for certain idealized situations (e.g., simple layered profiles) using constant head tests. However, variability in soil hydraulic properties could not be accurately determined for systems that exhibited more realistic stochastic heterogeneity. In this case, the heterogeneous profile could be replaced with an equivalent homogeneous profile and values of an effective isotropic saturated conductivity (Ks) and the shape parameter in the soil water retention function (α) could be inversely determined. The average value of Ksfor 100 stochastic realizations showed a similar dependency to I on σ, X, and Z. Whereas, the average value of α had large confidence interval for soil heterogeneity parameters and played a secondary role in drywell infiltration. This research provides valuable insight on the selection of site, design, installation, and long-term performance of a drywell.

The Effect of Geological Heterogeneity and Groundwater Table Depth on the Hydraulic Performance of Stormwater Infiltration Facilities

Urbanization has led to a substantial change in the hydrological cycle of urban catchments. Increased runoff and urban flooding, decreased direct subsurface infiltration and groundwater recharge, deterioration of water quality are among the major effects of this alteration. To alleviate these effects, Low Impact Development (LID) practices have been frequently adopted for stormwater management. Among LID infrastructures, infiltration facilities are particularly challenging to design and model due to the considerable amount of uncertainties related to the hydrogeological configuration of installation sites. To date, analysis on how soil heterogeneity, groundwater table depth, and thickness of the unsaturated zone affect the hydraulic performance of infiltration facilities are lacking. To address this knowledge gap, a series of numerical experiments under transient variably water saturated conditions were performed for a hypothetical infiltration facility. Numerical simulations showed that i) infiltration rates increase considerably as the initial depth of the groundwater table increases, ii) the contribution of the bottom of the facility to the infiltration of water is generally higher than the sides, iii) the presence of a less conducting soil layer at a short depth from the bottom of the facility reduces infiltration rates dramatically, iv) the complete clogging of the bottom of the facility has a dramatic impact on the hydraulic performance, v) the stochastic heterogeneity of the soil controls the overall stormwater infiltration process through the facility, and the hydraulic performance may largely deviate from the case when heterogeneity is absent.

Simulation of Channelized Gas Flow Pattern in Heterogeneous Porous Media: A Feasibility Study of Continuum Simulation at Bench Scale

Core Ideas A continuum model can predict quantitative and qualitative properties of gas flow patterns. Correlated spatial variability can capture dynamic features of gas flow channels. Connectivity metrics, like Euler number, provide a practical method for quantifying gas channels. In remediation technologies, air or O2 gas is injected into a polluted aquifer to remove organic contaminants. A gas injection process is also applied in enhanced oil recovery and CO2 sequestration. The wide range of gas injection processes into porous media necessitates accurate gas flow modeling. The focus of this study was to determine whether a continuum model with stochastic parameters can represent the properties of gas flow patterns. We applied stochastic heterogeneity in TOUGH2 simulation and used the experimental observations to validate simulation results. We created two types of stochastic heterogeneity: correlated heterogeneity, generated by an assigned covariance function, and uncorrelated heterogeneity, which distributes uniformly. We used Euler characteristics to quantify the gas channel properties and to determine whether the heterogeneity applied in a continuum model can represent gas channel properties. The results of this investigation confirm that the continuum model, which includes correlated heterogeneity, can predict the quantitative properties of gas flow, such as gas volume. Also, it can create gas channels that have Euler characteristics close to those obtained by experimental observation. In conclusion, the continuum model can predict the properties of gas flow if the spatial variability and correlation structure of the characteristic properties applied to the model are representative of the medium.

Single-cell RNA sequencing to explore immune cell heterogeneity.

Advances in single-cell RNA sequencing (scRNA-seq) have allowed for comprehensive analysis of the immune system. In this Review, we briefly describe the available scRNA-seq technologies together with their corresponding strengths and weaknesses. We discuss in depth how scRNA-seq can be used to deconvolve immune system heterogeneity by identifying novel distinct immune cell subsets in health and disease, characterizing stochastic heterogeneity within a cell population and building developmental 'trajectories' for immune cells. Finally, we discuss future directions of the field and present integrated approaches to complement molecular information from a single cell with studies of the environment, epigenetic state and cell lineage.

Abstract 886: An integrative platform for three-dimensional quantitative analysis of spatially heterogeneous metastasis landscapes

Abstract Metastatic microenvironments are spatially and compositionally heterogeneous. This seemingly stochastic heterogeneity provides researchers great challenges in elucidating factors that determine metastatic outgrowth. Herein, we develop and implement an integrative platform that will enable researchers to obtain novel insights from intricate metastatic landscapes. Our two-segment platform begins with whole tissue clearing, staining, and imaging to globally delineate metastatic landscape heterogeneity with spatial and molecular resolution. The second segment of our platform applies our custom-developed SMART 3D (Spatial filtering-based background removal and Multi-chAnnel forest classifiers-based 3D ReconsTruction), a multi-faceted image analysis pipeline, permitting quantitative interrogation of functional implications of heterogeneous metastatic landscape constituents, from subcellular features to multicellular structures, within our large three-dimensional (3D) image datasets. Coupling whole tissue imaging of brain metastasis animal models with SMART 3D, we demonstrate the capability of our integrative pipeline to reveal and quantify volumetric and spatial aspects of brain metastasis landscapes, including diverse tumor morphology, heterogeneous proliferative indices, metastasis-associated astrogliosis, and vasculature spatial distribution. Collectively, our study demonstrates the utility of our novel integrative platform to reveal and quantify the global spatial and volumetric characteristics of the 3D metastatic landscape with unparalleled accuracy, opening new opportunities for unbiased investigation of novel biological phenomena in situ. Citation Format: Ian H. Guldner, Lin Yang, Fang Liu, Danny Z. Chen, Siyuan Zhang. An integrative platform for three-dimensional quantitative analysis of spatially heterogeneous metastasis landscapes [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 886. doi:10.1158/1538-7445.AM2017-886

Reconciling seismicity and geodetic locking depths on the Anza section of the San Jacinto fault

AbstractObservations from the Anza section of the San Jacinto Fault in Southern California reveal that microseismicity extends to depths of 15–18 km, while the geodetically determined locking depth is less than ~10 km. This contrasts with observations from other major faults in the region and also with predictions of fault models assuming a simple layered distribution of frictional properties with depth. We suggest that an anomalously shallow geodetic fault locking may result from a transition zone at the bottom of seismogenic layer with spatially heterogeneous frictional properties. Numerical models of faults that incorporate stochastic heterogeneity at transitional depths successfully reproduce the observed depth relation between seismicity and geodetic locking, as well as complex spatiotemporal patterns of microseismicity with relatively scarce repeating earthquakes. Our models predict propagation of large earthquakes to the bottom of the transition zone, and ubiquitous aseismic transients below the locked zone, potentially observable using high‐precision geodetic techniques.

Modeling plasticity by non-continuous deformation

Plasticity and failure theories are still subjects of intense research. Engineering constitutive models on the macroscale which are based on micro characteristics are very much in need. This study is motivated by the observation that continuum assumptions in plasticity in which neighbour material elements are inseparable at all-time are physically impossible, since local detachments, slips and neighbour switching must operate, i.e. non-continuous deformation. Material microstructure is modelled herein by a set of point elements (particles) interacting with their neighbours. Each particle can detach from and/or attach with its neighbours during deformation. Simulations on two- dimensional configurations subjected to uniaxial compression cycle are conducted. Stochastic heterogeneity is controlled by a single “disorder” parameter. It was found that (a) macro response resembles typical elasto–plastic behaviour; (b) plastic energy is proportional to the number of detachments; (c) residual plastic strain is proportional to the number of attachments, and (d) volume is preserved, which is consistent with macro plastic deformation. Rigid body displacements of local groups of elements are also observed. Higher disorder decreases the macro elastic moduli and increases plastic energy. Evolution of anisotropic effects is obtained with no additional parameters.

An Integrative Platform for Three-dimensional Quantitative Analysis of Spatially Heterogeneous Metastasis Landscapes.

Metastatic microenvironments are spatially and compositionally heterogeneous. This seemingly stochastic heterogeneity provides researchers great challenges in elucidating factors that determine metastatic outgrowth. Herein, we develop and implement an integrative platform that will enable researchers to obtain novel insights from intricate metastatic landscapes. Our two-segment platform begins with whole tissue clearing, staining, and imaging to globally delineate metastatic landscape heterogeneity with spatial and molecular resolution. The second segment of our platform applies our custom-developed SMART 3D (Spatial filtering-based background removal and Multi-chAnnel forest classifiers-based 3D ReconsTruction), a multi-faceted image analysis pipeline, permitting quantitative interrogation of functional implications of heterogeneous metastatic landscape constituents, from subcellular features to multicellular structures, within our large three-dimensional (3D) image datasets. Coupling whole tissue imaging of brain metastasis animal models with SMART 3D, we demonstrate the capability of our integrative pipeline to reveal and quantify volumetric and spatial aspects of brain metastasis landscapes, including diverse tumor morphology, heterogeneous proliferative indices, metastasis-associated astrogliosis, and vasculature spatial distribution. Collectively, our study demonstrates the utility of our novel integrative platform to reveal and quantify the global spatial and volumetric characteristics of the 3D metastatic landscape with unparalleled accuracy, opening new opportunities for unbiased investigation of novel biological phenomena in situ.

Computational analysis of stochastic heterogeneity in PCR amplification efficiency revealed by single molecule barcoding.

The polymerase chain reaction (PCR) is one of the most widely used techniques in molecular biology. In combination with High Throughput Sequencing (HTS), PCR is widely used to quantify transcript abundance for RNA-seq, and in the context of analysis of T and B cell receptor repertoires. In this study, we combine DNA barcoding with HTS to quantify PCR output from individual target molecules. We develop computational tools that simulate both the PCR branching process itself, and the subsequent subsampling which typically occurs during HTS sequencing. We explore the influence of different types of heterogeneity on sequencing output, and compare them to experimental results where the efficiency of amplification is measured by barcodes uniquely identifying each molecule of starting template. Our results demonstrate that the PCR process introduces substantial amplification heterogeneity, independent of primer sequence and bulk experimental conditions. This heterogeneity can be attributed both to inherited differences between different template DNA molecules, and the inherent stochasticity of the PCR process. The results demonstrate that PCR heterogeneity arises even when reaction and substrate conditions are kept as constant as possible, and therefore single molecule barcoding is essential in order to derive reproducible quantitative results from any protocol combining PCR with HTS.

Commentary: Frailty and heterogeneity in epidemiological studies.

The paper by Aalen et al. is a timely discussion of an important topic. However, it conflates two concepts, frailty and heterogeneity, which are best kept apart. I would use the term frailty only when there is clear biological evidence that a fraction of the population is either exclusively at risk, or at vastly increased risk compared with the general population, of contracting a disease. An example of the former situation is cystic fibrosis, an autosomal recessive condition, which is caused only by inherited mutations in a single gene; an example of the latter is familial adenomatous polyposis (FAP) of the colon, a dominantly inherited condition that greatly increases the risk of colon cancer. Although there is no direct estimate of the relative hazard associated with FAP, it can be surmised to be several thousand and strongly age-dependent. I would reserve the term heterogeneity for inter-individual variation in susceptibility that is much more modest and arises from factors that do not clearly single out a sub-population at greatly increased risk of the disease. Heterogeneity of susceptibility may arise from biological factors, such as polymorphisms in metabolizing enzymes or interindividual variations in efficiency of DNA repair or cell proliferation, or from purely stochastic considerations. The role of stochasticity as a factor in heterogeneity has been under-appreciated. To their credit, Aalen et al. clearly recognize the importance of stochastic factors, and they correctly note that it is not easy to distinguish between stochasticity and chaotic behaviour arising from unstable dynamical systems. I prefer to work with stochastic models. Many toxicology experiments are conducted with highly inbred strains of animals kept under identical environmental conditions. Yet, despite identical ‘nature and nurture’, these animals do not succumb to disease at identical ages, and they show considerable heterogeneity in the number and size distribution of lesions.The same would presumably be true of humans subjected to similar experimental conditions. To summarize, there are three sources of inter-individual variation in susceptibility in human populations: first, at the most fundamental level, we have stochastic variations that are present even in genetically uniform populations living under similar or identical environmental conditions; second, we have inter-individual variations in the efficiency with which fundamental biological processes are carried out; and finally, large differences in susceptibility are determined by major gene defects (e.g. FAP) or by events occurring in embryonic life that alter populations of critical cells (perhaps exemplified by testicular carcinoma, as Aalen et al. note). Methods of analysis based on stochastic models of carcinogenesis automatically address stochastic heterogeneity if (and only if) the exact (stochastic) solutions to the models are used for data analyses. In this regard, I find the discussion of carcinogenesis models in this paper unclear. The models described in the papers by Heidenreich, Meza et al., Moolgavkar et al. and Armitage and Doll cited by Aaalen et al. were not developed to describe hazard functions in individuals, as the authors state, but rather in populations of like individuals. If the exact (stochastic) solution of these models is used in homogeneous populations, stochastic heterogeneity is immediately introduced. Let Xn-1 and Xn be random variables representing the number of pre-malignant and malignant cells, respectively, in a tissue at age t and let mn be the last mutation rate. Then, the exact stochastic solution to a carcinogenesis model is equivalent to solving the following expression for the hazard function, h(t)1⁄4 P’(t)/(1-P(t))1⁄4 mn*E[Xn-1 jXn1⁄4 0], where P(t) is the probability of a malignant cell at age t and E is the expectation. Quite often, approximate

Triadic closure as a basic generating mechanism of communities in complex networks.

Most of the complex social, technological, and biological networks have a significant community structure. Therefore the community structure of complex networks has to be considered as a universal property, together with the much explored small-world and scale-free properties of these networks. Despite the large interest in characterizing the community structures of real networks, not enough attention has been devoted to the detection of universal mechanisms able to spontaneously generate networks with communities. Triadic closure is a natural mechanism to make new connections, especially in social networks. Here we show that models of network growth based on simple triadic closure naturally lead to the emergence of community structure, together with fat-tailed distributions of node degree and high clustering coefficients. Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation. Communities are the more pronounced, the sparser the graph, and disappear for high values of link density and randomness in the attachment procedure. By introducing a fitness-based link attractivity for the nodes, we find a phase transition where communities disappear for high heterogeneity of the fitness distribution, but a different mesoscopic organization of the nodes emerges, with groups of nodes being shared between just a few superhubs, which attract most of the links of the system.

Complexity, confusion and controversy continue complicating the contribution of RyR2 channel phosphorylation to heart function.

Complexity, confusion and controversy continue complicating the contribution of RyR2 channel phosphorylation to heart function.

Mini-Workshop: Numerical Upscaling for Media with Deterministic and Stochastic Heterogeneity

This minisymposium was third in series of similar events, after two very successful meetings in 2005 and 2009. The aim was to provide a forum for an extensive discussion on the theoretical aspects and on the areas of application and validity of numerical upscaling approaches for heterogeneous problems with deterministic and stochastic coefficients. The intensive discussions during the meeting contributed to a better understanding of upscaling approaches for multiscale problems with stochastic coefficients, and for synergy between scientists coming to this topic from the area of deterministic multiscale problems on one hand, and those coming from the area of SPDE on the other hand. Recent advanced results on upscaling approaches for deterministic multiscale problems were presented, well mixed with strong presentations on SDE and SPDE. The open problems in these areas were discussed, with emphasis on the case of stochastic coefficients brainstorming numerous numerical upscaling approaches. A number of young researchers, very actively working in these areas, were involved in the workshop discussing the links between scales., thus ensuring the continuity between the generations of researchers.

In Situ Analysis of Heterogeneity in the Lipid Content of Single Green Microalgae in Alginate Hydrogel Microcapsules

Microalgae, a group of microorganisms that grow using sunlight as the sole energy source and carbon dioxide as an only carbon source, have been considered as a feedstock of choice for the production of biofuels such as biodiesel. To explore the economic feasibility of such application, however, many technical hurdles must first be overcome; the selection and/or screening of competent species are some of the most important and yet challenging tasks. To greatly accelerate this rather slow and laborious step, we developed a droplet-based microfluidic system that uses alginate hydrogel microcapsules with a mean diameter of 26 μm, each of which is able to encapsulate a single microalgal cell. This novel device was successfully demonstrated using three microalgae species, namely, Chlorella vulgaris , Chlamydomonas sp., and Botryococcus braunii . In situ analysis of the lipid content of individual microalgal cells by nondestructive fluorescence staining using BODIPY (4,4-difluoro-1,3,5,7,-tetramethyl-4-bora-3a,4a-diaza-s-indacene) was possible. In all cases, we confirmed that the lipid content of microalgal species in alginate hydrogel microcapsules was comparable to that of free-living cells. Stochastic heterogeneity in the lipid content was verified under a highly viable physiological condition, implying that other analyses were possible after the determination of lipid content. Furthermore, the designed microwell arrays enabled us to distinguish the BODIPY fluorescence response of a single live alga within the microcapsules.

Characterization of thermohaline staircases in the Tyrrhenian sea using stochastic heterogeneity mapping

We apply Stochastic Heterogeneity Mapping based on the band-limited von Kármán power law function to stacked migrated seismic data of thermohaline staircases in the Tyrrhenian Sea. This process allows the estimation of stochastic parameters such as the Hurst number (a measure of surface roughness) and scale length. Thermohaline staircases are regular, well-defined step-like variations in vertical profiles of temperature and salinity. In the ocean, they are thought to arise from double diffusion processes driven by the large difference in the molecular diffusivities of heat and salt. They are thought to have an anomalously weak internal wave-induced turbulence, making them suitable for the estimation of a lower detection limit of turbulent dissipation. The Tyrrhenian Sea is a natural laboratory for the study of such staircases because, due to the internal basin’s dynamic stability, steps as small as 10’s of meters can be seen. Lower Hurst numbers represent a richer range of higher wavenumbers corresponding to a broader range of heterogeneity in reflection events. We interpret a broader range of heterogeneity as indicative of a greater degree of turbulence.

Counterpoint: Alterations in airway smooth muscle phenotype do not cause airway hyperresponsiveness in asthma

We have been assigned the task of showing that “alterations in airway smooth muscle phenotype DO NOT cause the airways hyperresponsiveness of asthma.” In the following paragraphs we will briefly review the overwhelming lack of evidence that any fundamental change in the intrinsic properties of

The influence of dose heterogeneity on tumour control probability in fractionated radiation therapy

Theoretical modelling of tumour control probability (TCP) with respect to non-uniformity in the dose to the tumour, alternate fractionation schemes and tumour kinetics is a very useful tool for assessment of the influence of changes in dosimetric or radiobiological factors on the outcome of the treatment. Various attempts have been made to also include effects from non-uniform dose to the tumour volume, but the problem has not been fully solved and many factors were totally neglected or not accurately taken into account. This paper presents derivations of analytical expressions of TCP for macroscopic inter-cell dose variations and for random inter-fractional variations in average tumour dose, based on binomial statistics for the TCP and the well-known linear quadratic model for the cell survival. Numerical calculations have been performed to validate the analytical expressions. An analysis of the influence of the deterministic and stochastic heterogeneity in dose delivery on the TCP was performed. The precision requirements in dose delivery are discussed briefly with the support of the presented results. The main finding of this paper is that it is primarily the shape of the cell survival curve that governs how the response is affected by macroscopic dose variations. The analytical expressions for TCP accounting for heterogeneity in dose can quite well describe the TCP for varying dose from cell to cell and random dose in each fraction. An increased TCP is seen when a large number of fractions are used and the variations in dose to the cells are rather high for tissues with low α/β.

SAMPLING CONCRETE BY TOO SMALL ELEMENTS; WHAT SHOULD WE DO TO GET RELIABLE INFORMATION?

Macroscopically heterogeneous materials like concrete are generally sampled by too small, i.e., subrepresentative elements that can be either of 2D (section images) or of 3D nature (specimens). Based on scientific notions, like stochastic heterogeneity and structure-sensitivity, which are at the very heart of materials science and stereology, the paper demonstrates biases in obtained information to be generally inevitable when derived from such sub-representative designs. Only reliable comparison studies can be performed under the condition that the linear size of samples and of minimum structural dimensions (resulting from observation resolution) are maintained as fixed proportions of the relevant representative area and/or volume elements. This is demonstrated by three case studies.

MODERN ROUTES TO EXPLORE CONCRETE’S COMPLEX PORE SPACE

This paper concentrates on discrete element computer-simulation of concrete. It is argued on the basis of stochastic heterogeneity theory that modern concurrent-algorithm-based systems should be employed for the assessment of pore characteristics underlying durability performance of cementitious materials. The SPACE system was developed at Delft University of Technology for producing realistic schematizations of realcrete for a wide range of other particle packing problems, involving aggregate and fresh cement, and for the purpose of exploring characteristics in the hardened state of concrete, including of the pore network structure because of obvious durability problems. Since structure-sensitive properties are involved, schematization of reality should explicitly deal with the configuration of the cement particles in the fresh state. The paper concentrates on the stereological and mathematical morphology operations executed to acquire information on particle size, global porosity, and on distribution of porosity and of the connected pore fraction as a result of the near neighbourhood of aggregate grains. Goal is to provide information obtained along different exploration routes of concrete's pore space for setting up a pore network modelling approach. This type of methodological papers is scarce in concrete technology, if not missing at all. Technical publications that report on obtained results in our investigations are systematically referred to.