Data-driven Global Sensitivity Analysis of Three- Phase Distribution System with PVs

Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

In this study, a hybrid metamodel using the orthogonal constraints of radial basis function and sparse polynomial chaos expansions is proposed for the global sensitivity analysis of time-consuming models. Firstly, the orthogonal conditions of radial basis functions (RBF) and polynomial chaos expansions (PCE) were derived to construct the hybrid metamodel. Then, the variance of the metamodel was decoupled into the variances of the RBF and PCE independently by using the orthogonal condition. Furthermore, the analytical formulations of Sobol indices for the hybrid metamodel were derived according to the orthogonal decomposition. Thus, the interaction items of radial basis function and polynomial chaos expansions were eliminated, which significantly simplifies the Sobol indices. Two analytical cases were employed to investigate the influence of the number of the polynomial chaos expansions items, and several analytical and engineering cases were tested to demonstrate the accuracy and efficiency of the proposed method. In the engineering cases, the proposed method yielded significant improvements in terms of both accuracy and efficiency comparing with the existing global sensitivity analysis approaches, which indicates that the proposed method is more appropriate to the global sensitivity analysis of time-consuming engineering problems.

Mixed kernel function support vector regression for global sensitivity analysis

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

Global sensitivity analysis in high dimensions with PLS-PCE

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

The main focus of this thesis is the uncertainty propagation (UP) and global sensitivity analysis (GSA) in complex hydrogeological numerical models. Various methods are presented with applications on numerical models for the groundwater flow and mean lifetime expectancy (MLE) in the scope of Andra's (French National Radioactive Waste Management Agency) project for the geological disposal of high-level and intermediate-level long-lived radioactive wastes in a highly impermeable layer from Callovo-Oxfordian age (COX) in France. <br> A state of the art is provided for the theory of uncertainty propagation and for the methodologies of sensitivity analyses in a broad sense. Methods for UP are provided from 2-levels Factorial Designs to quasi-random samplings. GSA techniques encompass screening methods such as the Morris Measures and the Derivative-based Global Sensitivity Measures (DGSM), and also the so-called Sobol' indices based upon the variance decomposition of the response of interest. Meta-modelling techniques such as polynomial regression and Polynomial Chaos Expansions (PCE) meta-models are employed as surrogate models for UP and GSA purpose at negligible computational-costs. A comparison of GSA techniques upon various complex analytical test-functions was undertaken with the purpose of determining a relevant method to be employed in the context of “screening” out unimportant variables in computer-intensive, high-dimensional models. <br> A numerical model of groundwater flow and lifetime expectancy is employed for assessing the effect of uncertain advection-dispersion parameters and their spatial distributions upon the MLE from a target zone inside the domain. The model is a 2-dimensions synthetic cross-section of the eastern region of the Paris Basin (Meuse/Haute-Marne sector). This model was used as an exploratory tool for sensitivity analysis methods applied upon numerous sets of uncertain hydrodynamic and dispersion parameters in 15 layers. The uncertainty characterizing the permeability-porosity values in aquifer formations encompassing the COX have proved to add much of variability to the MLE calculated from the target zone. The model also served at exploring the effect of the spatial variability of permeability-porosity parameters in two main aquifer sequences on the groundwater flow rates and MLE in the model. The variabilities of the output responses are mainly due to the uncertainty upon the means and variances of the permeability-porosity distributions, as well as the longitudinal correlation lengths, in each sequence. <br> Then, a 3-dimensions high-definition hydrogeological model representing the Meuse/Haute-Marne sector in the eastern region of the Paris Basin is a more comprehensive numerical model incorporating realistic geometries, fractures, heterogeneities and discontinuities encountered on field. A sensitivity analysis of the MLE from a given zone located in the middle of the COX layer was performed by perturbing the hydraulic conductivities and porosities values in fourteen hydrogeological formations. The uncertain permeability-porosity parameters in the aquifer formations from Bathonian in the Dogger sequence, and Rauracian-Sequanian in the Oxfordian sequence, have strong and rather non-linear effects on the variability of the output response of interest. <br> The methodologies for UP and GSA employed in the present thesis have proved to be very efficient when applied to large hydrogeological models of groundwater flow and MLE. In particular, quasi-random sampling methods offer a flexible frame for providing the uncertainty distribution of the output response of interest at low computational costs. Screening techniques provide a fast estimation for the overall contribution of each input variable to the variability of the output. Meta-modelling techniques such as PCE proved highly accurate in individualising the low- and high-order effects of each input variable upon the output response of interest.

Development of a behaviour-pattern based global sensitivity analysis procedure for coupled socioeconomic and environmental models

Global sensitivity analysis and uncertainty quantification of soot formation in an n-dodecane spray flame

We perform global sensitivity analysis (GSA) through polynomial chaos expansion (PCE) on a contaminant transport model for the assessment of radionuclide concentration at a given control location in a heterogeneous aquifer, following a release from a near surface repository of radioactive waste. The aquifer hydraulic conductivity is modeled as a stationary stochastic process in space. We examine the uncertainty in the first two (ensemble) moments of the peak concentration, as a consequence of incomplete knowledge of (a) the parameters characterizing the variogram of hydraulic conductivity, (b) the partition coefficient associated with the migrating radionuclide, and (c) dispersivity parameters at the scale of interest. These quantities are treated as random variables and a variance-based GSA is performed in a numerical Monte Carlo framework. This entails solving groundwater flow and transport processes within an ensemble of hydraulic conductivity realizations generated upon sampling the space of the considered random variables. The Sobol indices are adopted as sensitivity measures to provide an estimate of the role of uncertain parameters on the (ensemble) target moments. Calculation of the indices is performed by employing PCE as a surrogate model of the migration process to reduce the computational burden. We show that the proposed methodology (a) allows identifying the influence of uncertain parameters on key statistical moments of the peak concentration (b) enables extending the number of Monte Carlo iterations to attain convergence of the (ensemble) target moments, and (c) leads to considerable saving of computational time while keeping acceptable accuracy.

Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

Significant variables affecting the performance of concrete panels impacted by wind-borne projectiles: A global sensitivity analysis

Full text Figures and data Side by side Abstract Editor's evaluation Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract Collective cell migration plays an essential role in vertebrate development, yet the extent to which dynamically changing microenvironments influence this phenomenon remains unclear. Observations of the distribution of the extracellular matrix (ECM) component fibronectin during the migration of loosely connected neural crest cells (NCCs) lead us to hypothesize that NCC remodeling of an initially punctate ECM creates a scaffold for trailing cells, enabling them to form robust and coherent stream patterns. We evaluate this idea in a theoretical setting by developing an individual-based computational model that incorporates reciprocal interactions between NCCs and their ECM. ECM remodeling, haptotaxis, contact guidance, and cell-cell repulsion are sufficient for cells to establish streams in silico, however, additional mechanisms, such as chemotaxis, are required to consistently guide cells along the correct target corridor. Further model investigations imply that contact guidance and differential cell-cell repulsion between leader and follower cells are key contributors to robust collective cell migration by preventing stream breakage. Global sensitivity analysis and simulated gain- and loss-of-function experiments suggest that long-distance migration without jamming is most likely to occur when leading cells specialize in creating ECM fibers, and trailing cells specialize in responding to environmental cues by upregulating mechanisms such as contact guidance. Editor's evaluation This important study presents predictions from a computational model demonstrating the impact of the extracellular matrix on collective cell migration in the neural crest. The evidence supporting the claims of the authors is solid, and the study is interesting to cell biologists exploring cell migration in different contexts. https://doi.org/10.7554/eLife.83792.sa0 Decision letter eLife's review process Introduction Vertebrate neural crest cells (NCCs) are an important model for collective cell migration. Discrete streams of migratory NCCs distribute throughout the embryo to contribute to nearly every organ (Le Douarin and Kalcheim, 1999; Tang and Bronner, 2020). Consequently, mistakes in NCC migration may result in severe birth defects, termed neurocristopathies (Vega-Lopez et al., 2018). In contrast to well-studied tightly adhered cell cluster models, such as border cell and lateral line migration (Peercy and Starz-Gaiano, 2020; Olson and Nechiporuk, 2021), much less is known about how ‘loosely’ connected cells, such as NCCs, invade through immature extracellular matrix (ECM) and communicate with neighbors to migrate collectively. Moreover, several invasive mesenchymal cancers resemble collective NCC migration, with cells moving away from the tumor mass in chain-like arrays or narrow strands (Friedl et al., 2004; Friedl and Alexander, 2011). Therefore, utilizing the neural crest experimental model to gain a deeper knowledge of the cellular and molecular mechanisms underlying collective cell migration has the potential to improve the repair of human birth defects and inform strategies for controlling cancer cell invasion and metastasis. Time-lapse analyses of NCC migratory behaviors in several embryo model organisms have revealed that leader NCCs in discrete migratory streams in the head (Teddy and Kulesa, 2004; Genuth et al., 2018), gut (Druckenbrod and Epstein, 2007; Young et al., 2014), and trunk (Kasemeier-Kulesa et al., 2005; Li et al., 2019) are highly exploratory. Leading NCCs extend thin filopodial protrusions in many directions, interact with the ECM and other cell types, then select a preferred direction for invasion. Trailing cells extend protrusions to contact leaders and other cells to maintain cell neighbor relationships and move collectively (Kulesa et al., 2008; Ridenour et al., 2014; Richardson et al., 2016). These observations suggest a leader-follower model for NCC migration (McLennan et al., 2012) in which NCCs at the front of migrating collectives read out guidance signals and communicate over long distances with trailing cells. This model challenged other proposals that NCCs respond to a chemical gradient signal and sustain cohesive movement via an interplay of local cell co-attraction and contact inhibition of locomotion (Theveneau and Mayor, 2012; Szabó et al., 2016; Merchant et al., 2018; Merchant and Feng, 2020). The precise cellular mechanisms that underlie leader-follower migration behavior, for example, the involvement with ECM or the nature of communication signals created by leaders, have not been elucidated. One paradigm that has emerged suggests that loosely connected streams of NCCs move in a collective manner by leaders communicating through long-range signals that are interpreted and amplified by follower NCCs. In support of this, chick leader cranial NCCs show enhanced expression of secreted factors, such as angiopoietin-2 (Ang-2) (McLennan et al., 2015a) and fibronectin (FN) (Morrison et al., 2017). Knockdown of Ang-2 reduces the chemokinetic behavior of follower chick NCCs, resulting in disrupted collective cell migration (McKinney et al., 2016). These observations suggest that follower NCC collective movement depends on signals deposited in the microenvironment by leaders or the adjacent mesoderm. Signals in the FN-rich ECM may also provide microenvironmental cues for NCC collective migration. NCCs cultured in FN-rich ECM move with thin, anchored filopodia through a field that is punctate immediately distal to the migrating front, while ‘pioneer’ NCCs within the front appear to form radially oriented bundles of FN-containing filaments (Rovasio et al., 1983). Later work on the NCC epithelial-to-mesenchymal transition showed that inhibition of ECM-integrin receptors resulted in delamination of NCCs into the neural tube lumen (Kil et al., 1996). Moreover, FN is abundant in the mouse head and neck (Mittal et al., 2010), and there is a dramatic reduction in the number of migrating NCCs that reach the heart in FN null mice (Wang and Astrof, 2016). Thus, FN is critical for NCC to reach their targets, although its precise role in collective cell migration remains unclear. Mathematical modeling of NCC migration can help provide insight into the role of FN and identify the origins of multiscale collective behaviors (Giniūnaitė et al., 2020; Kulesa et al., 2021). Previous models for NCC migration demonstrated that contact guidance, a mechanism by which cells align themselves along ECM fibers, can establish collective behavior and create single-file cell chains (Painter, 2009). Later models incorporating ECM degradation and haptotaxis, a process by which cells migrate up adhesive ECM gradients, demonstrated how matrix heterogeneity and cell-cell interactions could determine cell migratory patterns (Painter et al., 2010; Wynn et al., 2013). Models for other collectively migrating cells, such as fibroblasts, suggest that ECM remodeling by motile cells can enable anisotropic collective movement, with migratory directions dictated by fiber orientation (Dallon et al., 1999; Groh and Louis, 2010; Chauviere et al., 2010; Azimzade et al., 2019; Wershof et al., 2019; Pramanik et al., 2021; Suveges et al., 2021; Metzcar et al., 2022). No models have yet addressed how collective migration arises from cell remodeling of an initially isotropic, immature ECM. In this paper, we develop an agent-based model (ABM; also known as an individual-based model) of chick cranial NCC migration that considers a cell-reinforced migratory cue in which ‘leader’ cells remodel an initially punctate and immature FN matrix to signal ‘follower’ cells. Other processes detailed in the model include cell-cell repulsion, haptotaxis, and contact guidance. This framework incorporates new observations of FN distribution in the chick cranial NCC microenvironment and simulates gain- and loss-of-function of FN. Detailed simulations of the model over parameter space, coupled with global sensitivity analysis of ABM parameters, identifies mechanisms that dominate the formation of migrating streams and other NCC macroscopic behavior. Through this analysis, we find that migration is most efficient when leading NCCs specialize in remodeling FN to steer the collective, as cells otherwise enter a ‘jammed’ state in which migration is greatly reduced and cells are densely packed together (Sadati et al., 2013). The addition of ‘guiding signals’ that direct NCCs along a target corridor limits excessive lateral migration in the ABM but concurrently promotes separation between leader and trailing cells in the stream. We survey ABM parameter combinations that recover robust collective migration without such stream breaks, which underscore the potential importance of contact guidance. Results FN protein expression within the mesoderm is unorganized and punctate prior to cranial NCC emigration, but filamentous after it has been traversed by leader cells We confirmed that FN throughout the head, neck and cardiovascular regions in the chick embryo is distributed in patterns that overlap with NCC migratory pathways (Figure 1; Duband and Thiery, 1982). To assess the in vivo distribution of FN protein at higher spatial resolution, we examined transverse cryosections (Figure 1A; Hamburger and Hamilation, 1951) at developmental stages (HH12–13) midway through cranial NCC migration to reveal that NCCs are in close association with a heterogeneous meshwork of FN (Figure 1B). Punctate FN, not yet fibrils, are found both distal to the invasive NCC migratory front and adjacent to the leader NCC subpopulation (Figure 1C). By contrast, elongated FN fibrils are located behind the leading edge of invasive NCC streams (Figure 1D). FN fibrils proximal to the invasive NCC migratory front did not reveal a preferred directional orientation. Similar punctate FN was also visible in regions outside the NCC migratory pathway, subjacent to the surface ectoderm (Figure 1C). Figure 1 with 1 supplement see all Download asset Open asset In vivo observations of fibronectin (FN) and results from gain/loss-of-function experiments. (A) Schematic of a typical neural crest cell (NCC) migratory stream in the vertebrate head of the chick embryo, at developmental stage HH12–13 (Hamburger and Hamilation, 1951) at the axial level of the second branchial arch (ba2). (B) Transverse section through the NCC migratory stream at the axial level of rhombomere 4 (r4) triple-labeled for FN (green), nuclei (DAPI-blue) and migrating NCCs (HNK1-red). NCCs migrate subjacent to the surface ectoderm after emerging from the dorsal neural tube (NT). The arrowhead points to the surface ectoderm. The yellow boxes highlight the tissue subregions that contain the leader NCCs (box 1) and are distal to the leader NCCs (box 2), marking distinct shapes of the FN in each box with an asterisk (box 1) and open circle (box 2). (C) FN only. (D) The fibrous (box 1-asterisk) and punctate (box 2-open circle) appearance of FN in the NCC microenvironment. (E) NCC distance migrated in FN morpholino-injected embryos and (F) percentage area of the NCC migratory stream after microinjection of soluble FN into the r4 paraxial mesoderm prior to NCC emigration. NT = neural tube. The scale bars are 50 µm (B–C) and 10 µm (D). Gain- or loss-of-function of FN leads to reduced NCC migration Functional analysis confirms FN is required for normal NCC migration. Knockdown of FN expression introduced into premigratory NCCs within the neural tube led to a significant reduction (nearly 30%) in the total distance migrated by NCCs enroute to BA2 (Figure 1E). Microinjection of soluble FN into the cranial NCC migratory domain, for example, into the paraxial mesoderm adjacent to rhombomere 4 (r4) prior to NCC delamination, also led to a dramatic reduction (by 70%) in NCC migration as indicated by a decrease in the area typically covered by the invading NCCs (Figure 1F). Thus, decreasing the expression of FN – presumably by decreasing the rate at which FN is secreted by motile NCCs – or increasing the FN density in the microenvironment led to significant changes in the NCC migration pattern. We conclude that a balance of FN within the migratory microenvironment is required to promote proper migration. An individual-based model of NCC migration and ECM remodeling produces collectively migrating streams in silico Our observations led us to hypothesize that migrating NCCs remodel punctate FN into a fibrous scaffold for trailing cells. We evaluated this idea in a theoretical setting by constructing a mathematical model in which NCCs are represented as discrete off-lattice point masses, that is, agents, that freely move in a two-dimensional (2D) plane (Figure 2—figure supplement 1). Each agent responds to, and influences, the remodeling of an initially punctate ECM (Figure 2; Figure 2—figure supplement 2). Their velocities are determined using an overdamped version of Newton’s second law. The three types of forces that alter agent trajectories arise from friction (which is proportional to the cell velocity), cell-ECM interactions (specifically, those from haptotaxis and contact guidance), and cell-cell repulsion. Neighboring NCCs, FN puncta, and FN fibers generate the latter two forces and affect the motion of an agent only when they are within a user-specified distance, Rfilo , of the agent center (this distance represents the length of cell filopodia protrusions). Figure 2 with 13 supplements see all Download asset Open asset Integration of extracellular matrix (ECM) within an agent-based model (ABM) of neural crest cell (NCC) migration. Individual snapshots (A) of an example ABM realization reveals that the model can generate a single anisotropically migrating stream over a simulated time of 12 hr. Different realizations generated using the same parameter values but different random seeds (B), however, may produce streams that exhibit the formation of multiple branches and demonstrate the range of possible model behaviors. Black circles denote leader cells, which can secrete new FN, red cells signify follower non-secretory cells, and blue squares correspond to FN puncta. Arrows denote cell velocities or fiber orientations. The extra column of FN at the right boundary is an artifact of visualization. Sobol indices (C) and scatter plots (D) of the horizontal distance traveled by NCCs indicate that this metric is most sensitive to the haptotaxis-contact guidance weight, χ, and the filopodial length, Rfilo , but is less dependent on parameters related to cell-cell repulsion (ci). Statistical significance in (C) is determined from a two-sample t-test that compares the Sobol indices produced by the parameter of interest to those obtained from a dummy parameter (red asterisks indicate significant first-order indices, black asterisks indicate significant total order indices, p<0.01). Each data point in (D) represents the average of 20 ABM realizations. The cell-repulsion (resp. cell-ECM) force accounts for the collective interactions that an agent experiences from neighboring NCCs (resp. FN puncta and fibers). The magnitude of the total cell-cell repulsion force is determined from the sum of radially oriented forces from all neighboring NCCs, whose strength, modulated by a user-defined constant, ci , decreases quadratically with respect to the distance from the agent center of mass. To represent the finding that chick cranial NCCs do not always repel each other upon contact (Kulesa and Fraser, 1998; Kulesa et al., 2004), we adjust the direction of the resultant force by stochastically sampling from a von Mises distribution (Mardia and Jupp, 1999). The parameters of the distribution depend on the number and location of NCCs sensed by the agent. They ensure it is uniform when few NCCs are present but cause it to resemble a periodic normal distribution biased in the direction of lowest NCC density when many cells are sensed (for details, see the Materials and methods section). Thus, when cells sense each other at longer ranges, they may align. When cells are close enough to be overlapping, however, they are more likely to repel each other along the direction of contact, similarly to other implementations of cell-cell repulsion (Colombi et al., 2020). We have verified that increasing the magnitude of the cell-cell repulsion forces increases the average nearest neighbor distance between cells in the ABM (Figure 2—figure supplement 5; Figure 3—figure supplement 4). The magnitude of the total cell-ECM force is similarly determined by summing radially oriented forces originating from neighboring FN puncta and fibers, with the strengths of such forces decreasing quadratically with respect to distance from the agent center. The resultant cell-ECM force direction is determined by a linear combination of signals arising from haptotaxis and contact guidance, which are weighted by a parameter, χ. The haptotaxis and contact guidance cues are both represented as unit vectors. Haptotaxis biases the total cell-ECM force toward increasing FN densities and its cue is sampled from a von Mises distribution whose parameters depend on the number and location of neighboring FN puncta and fibers sensed by the cell. The distribution is biased such that the cell is likely to travel toward the greatest FN concentration sampled. Contact guidance aligns the cell-ECM force along the direction of FN fibers. The unit vector corresponding to this cue is computed from the average orientation of FN fibers sensed by the agent. Cells migrate through an initially isotropic, equi-spaced, square lattice of FN puncta that approximates the matrix distribution prior to NCC migration. Leader cells are represented by a fixed number of ‘secretory’ cells that generate new FN puncta at their centers according to times drawn from an exponential distribution with user-specified mean. The cells start at the left-hand boundary of the lattice, which we take to represent the section of the neural tube located along r4. Non-secretory cells, which cannot create new FN puncta, enter the domain at later times, provided sufficient space is available. We note that the terms ‘secretory’ and ‘non-secretory’ refer only to the ability of cells to secrete new FN puncta, as both cell types can create and align fibers emanating from puncta they pass over. Observations of individual ABM simulations indicate that ECM remodeling, haptotaxis, contact guidance, and cell-cell repulsion can generate stream-like patterns, with secretory cells able to maintain their positions at the front of the stream (Figure 2A; Figure 2—video 1). Cells can migrate the FN lattice is isotropic, and trailing cell velocities are oriented toward leader cells (for the average that the follower cell vector with the horizontal is or for the in Figure patterns most ECM fibers to the horizontal that is, the direction of the target corridor (Figure 2—figure supplements Figure 2—video NCCs do not always maintain a single mass as they migrate collectively. In ABM streams into two or more that regions along the (Figure Figure 2 and 4). there is signal NCCs in a direction to the horizontal Thus, in cells may sense and travel toward FN puncta located to the target corridor. We conclude that additional signals are required to NCC stream In later we how such signals affect the of patterns by NCCs. Global sensitivity analysis suggests a key role for contact guidance in long-distance NCC migration To determine how collective migration depends on ABM parameters, we sensitivity et al., to for collective migration. This analysis Sobol indices (Figure which the by which the of a is to changes in a parameter of interest values indicate that the is more sensitive to the The analysis produces two types of Sobol first-order indices, which the of to a parameter of and indices, which include additional that arise when other parameters are The resulting Sobol indices indicate that the distance NCCs travel in the horizontal direction along the target is most sensitive to χ, the parameter the to which NCC directional migration in response to the FN matrix is by haptotaxis contact guidance or a linear combination of the the of this parameter decreases the distance cells travel The cell filopodial Rfilo , the Sobol indices and a increasing with the This as increasing the number of FN puncta and fibers that the cell be to generate more and migration in the The parameter for the cell-cell repulsion force strength, ci , presents a but significant first-order analysis of its scatter (Figure reveals that when contact guidance the cell-ECM force increasing the cell-cell repulsion decreases the distance that the streams migrate When haptotaxis the direction of the force this is but remains decreasing the distance traveled by NCCs is most sensitive to the mechanism by which cells respond to the with contact guidance longer while haptotaxis and cell-cell repulsion are with the distance that NCCs We results for a the extent of the migrating stream in directions to the target that the lateral of cells in the ABM from the target corridor (Figure 2—figure supplement we refer to this as the The cell-ECM weight, χ, the Sobol indices for this and a that lateral migration increases with of contact guidance. By contrast, scatter plots suggest this is with the filopodial and cell-cell repulsion of Sobol indices for the average distance between neighboring cells reveals the importance of haptotaxis and cell-cell repulsion on cell The cell-ECM and the cell-cell repulsion parameter both significant first-order Sobol indices (Figure 2—figure supplement with the latter parameter the Sobol is significant for the filopodial which that this parameter cell-cell separation via its interactions with the other two This that the cell-ECM and cell-cell repulsion forces are by changing the number of FN puncta and NCCs plots (Figure 2—figure supplement suggest a decreasing between the nearest neighbor distance and the cell-ECM weight, a increasing with the cell-cell repulsion parameter, ci and for the filopodial Leading NCCs collective migration by and remodeling ECM To identify combinations of parameters that collective migration, we simulated experimental that affect cell of new FN (Figure see Materials and while cell of fibers from puncta When leader secretory cells secrete FN puncta more we find that the stream by By contrast, cell new FN puncta, then the average distance the stream decreases by about migration cells can respond to both cell types secrete FN, such that there is between cell then the average distance migrated by cells decreases from the of at the rate or is Similar results for the lateral of NCCs (Figure 3—figure supplement 1). Figure with 4 supplements see all Download asset Open asset distance traveled by neural crest cells (NCCs) after 12 hr. plots for experiments in which (A) fibronectin (FN) is (B) and fiber are and (C) cells invade a FN lattice suggest that the extracellular matrix (ECM) plays an important role in NCC migration. experiments decrease the average over which a cell new FN from to 10 Contact guidance and cell-cell repulsion in (C) correspond to and indicate are different from that of the parameter using a agent-based model (ABM) realizations are to generate each We how cells alter the FN by both FN and fiber in leader follower cells (Figure When leading secretory cells both cell are to remodel the the average distance traveled by the NCC stream decreases by (resp. When follower ‘non-secretory’ cells are from and FN fibers, however, the is with only a reduction in distance Similar results are for the nearest neighbor distance and the lateral of NCCs (Figure 3—figure supplement 2). These results demonstrate within the FN remodeling by leading NCCs plays a key role in long-distance collective migration. By contrast, are when trailing cells cannot remodel the Our suggest that collective migration may be more when leading and trailing NCCs with leading cells remodeling the ECM. The FN matrix distribution is to long-distance collective cell migration ECM remodeling can direct collective cell migration, but the to which the ECM cell trajectories remains unclear. the lattice between FN puncta from 20 to µm collective migration in the decreasing the distance that the stream by The lateral of NCCs is similarly reduced within (Figure 3—figure supplement We conclude that NCCs are less likely to sense FN in their local then they are less likely to migrate as the nearest neighbor distance between cells decreases (Figure 3—figure supplement an cell density and state a in which cells are tightly to movement, and a (Sadati et al., 2013). These lead us to cells in the ABM as in a ‘jammed’ state when they collectively travel less µm over 12 as we have found a but significant between the nearest neighbor distance and the distance traveled in the horizontal direction (Figure 2—figure supplement Figure 3—figure supplement 4). Cells however, mechanisms to for FN and long-distance collective migration (Figure contact guidance is in the ABM the decreases from to then the NCC migration distance in FN increases by The distance that obtained in the FN lattice by the cell-cell repulsion or the rate at which secretory cells produce FN also cause NCCs to travel distances within the FN matrix (by and but changes do not migration to distances to those in These results highlight the importance of contact guidance, ECM remodeling, cell-cell repulsion in long-distance migration, when cells are in a state migration is otherwise directional guidance cells along their target but the model sensitive to stream and cell separation mechanisms that generate collective migration do not that cells travel along a single

Simulation of fate and transport mechanisms in the porous systems from contaminant transport models are affected by uncertainty associated with input model parameters. Sensitivity analysis (SA) provides tools to quantify the sources of uncertainty to the variations in the model output metrics. To quantify the uncertainty associated with physical non-equilibrium contaminant transport model, global SA was conducted for the problem mimicking reactive transport in the saturated soil column conditions. Five global SA methods, namely Morris, RSA (Regionalized Sensitivity Analysis), Sobol, FAST (Fourier Amplitude Sensitivity Test), and PAWN, were tested based on the temporal moments of contaminant concentrations for two output metrics: zeroth temporal moment (ZTM) and mean residence time (MRT). The ranking order of ten input model parameters from global SA methods for two output metrics was compared. Morris SA implied that the ZTM at outlet of the soil column is highly sensitive to sorption distribution coefficient in the mobile and immobile regions and less sensitive to dispersion coefficient and degradation rate constant in the immobile region. The mass-transfer coefficient showed highest non-linear interactions with other flow and transport parameters based on the highest value of standard deviation of elementary effects (EEs) for ZTM output metric. The sorption distribution coefficient in the mobile region and mass-transfer coefficient showed highest sensitivity and non-linear effect toward MRT based on the Morris method. The comparison of global SA methods revealed that the top two sensitive parameters affecting ZTM and MRT were the same from all the considered methods. However, large difference in the ranking order of bottom three sensitive parameters was observed. The sorption distribution coefficient of mobile region and mass-transfer coefficient were observed as the most sensitive parameters affecting ZTM and MRT based on the comparison of all five global SA methods. Overall results suggest that the non-linear contaminant transport model should be examined based on multiple sensitivity output metrics via a multi-model approach. The multi-model global SA approach implemented in this study highlighted its significance in quantifying the interplay of non-linear model parameters.

Reservoir stimulation is a widely used technique in the oil and gas industry for increasing the productivity of hydrocarbon reservoirs, most notably in carbonate formations. This work aims to develop an optimization workflow under uncertainty for matrix acidizing. A reactive transport model is implemented in a finite-element framework to simulate the initiation and propagation of dissolution channels in porous carbonate rock. The model is verified using an analytical solution. We utilize surrogate modeling based on polynomial chaos expansion (PCE) and Sobol indices to identify the most significant parameters. We investigate the effect of varying 12 identified parameters on the efficiency of the stimulation process using dimensionless groups, including the Damköhler, Peclet, and acid capacity numbers. Furthermore, the surrogate model reproduces the physics-based results accurately, including the dissolution channels, the pore volume to breakthrough, and the effective permeability of the stimulated rock. The developed workflow assesses how uncertainties propagate to the model's response, where the surrogate model is used to calculate the univariate effect. The global sensitivity analysis shows that the acid capacity number is the most significant parameter for the pore volume to breakthrough with the highest Sobol index. The marginal effect calculated for the individual parameter confirms the results from Sobol indices. This work provides a systematic workflow for uncertainty analysis and optimization applied to the processes of rock stimulation. Characterizing the impact of uncertainty provides physical insights and a better understanding of the matrix acidizing process.