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Chakraborty D, Gutierrez‐Chakraborty E, Rodriguez‐Aguayo C, Başağaoğlu H, Lopez‐Berestein G, Amero P. Discovering genetic biomarkers for targeted cancer therapeutics with eXplainable Artificial Intelligence. Cancer Commun (Lond) 2024; 44:584-588. [PMID: 38566430 PMCID: PMC11110951 DOI: 10.1002/cac2.12530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Revised: 01/12/2024] [Accepted: 02/29/2024] [Indexed: 04/04/2024] Open
Affiliation(s)
- Debaditya Chakraborty
- School of Civil and Environmental Engineering and Construction ManagementThe University of Texas at San AntonioSan AntonioTexasUSA
| | | | - Cristian Rodriguez‐Aguayo
- Department of Experimental TherapeuticsThe University of Texas MD Anderson Cancer CenterHoustonTexasUSA
| | | | - Gabriel Lopez‐Berestein
- Department of Experimental TherapeuticsThe University of Texas MD Anderson Cancer CenterHoustonTexasUSA
| | - Paola Amero
- Department of Experimental TherapeuticsThe University of Texas MD Anderson Cancer CenterHoustonTexasUSA
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Chakraborty D, Gutierrez-Chakraborty E, Rodriguez-Aguayo C, Başağaoğlu H, Lopez-Berestein G, Amero P. Discovering genetic biomarkers for targeted cancer therapeutics with eXplainable AI. bioRxiv 2023:2023.07.24.550346. [PMID: 37546729 PMCID: PMC10402052 DOI: 10.1101/2023.07.24.550346] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/08/2023]
Abstract
Explainable Artificial Intelligence (XAI) enables a holistic understanding of the complex and nonlinear relationships between genes and prognostic outcomes of cancer patients. In this study, we focus on a distinct aspect of XAI - to generate accurate and biologically relevant hypotheses and provide a shorter and more creative path to advance medical research. We present an XAI-driven approach to discover otherwise unknown genetic biomarkers as potential therapeutic targets in high-grade serous ovarian cancer, evidenced by the discovery of IL27RA, which leads to reduced peritoneal metastases when knocked down in tumor-carrying mice given IL27-siRNA-DOPC nanoparticles. Summary Explainable Artificial Intelligence is amenable to generating biologically relevant testable hypotheses despite their limitations due to explanations originating from post hoc realizations.
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Chakraborty D, Ivan C, Amero P, Khan M, Rodriguez-Aguayo C, Başağaoğlu H, Lopez-Berestein G. Explainable Artificial Intelligence Reveals Novel Insight into Tumor Microenvironment Conditions Linked with Better Prognosis in Patients with Breast Cancer. Cancers (Basel) 2021; 13:3450. [PMID: 34298668 PMCID: PMC8303703 DOI: 10.3390/cancers13143450] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Revised: 07/06/2021] [Accepted: 07/06/2021] [Indexed: 12/29/2022] Open
Abstract
We investigated the data-driven relationship between immune cell composition in the tumor microenvironment (TME) and the ≥5-year survival rates of breast cancer patients using explainable artificial intelligence (XAI) models. We acquired TCGA breast invasive carcinoma data from the cbioPortal and retrieved immune cell composition estimates from bulk RNA sequencing data from TIMER2.0 based on EPIC, CIBERSORT, TIMER, and xCell computational methods. Novel insights derived from our XAI model showed that B cells, CD8+ T cells, M0 macrophages, and NK T cells are the most critical TME features for enhanced prognosis of breast cancer patients. Our XAI model also revealed the inflection points of these critical TME features, above or below which ≥5-year survival rates improve. Subsequently, we ascertained the conditional probabilities of ≥5-year survival under specific conditions inferred from the inflection points. In particular, the XAI models revealed that the B cell fraction (relative to all cells in a sample) exceeding 0.025, M0 macrophage fraction (relative to the total immune cell content) below 0.05, and NK T cell and CD8+ T cell fractions (based on cancer type-specific arbitrary units) above 0.075 and 0.25, respectively, in the TME could enhance the ≥5-year survival in breast cancer patients. The findings could lead to accurate clinical predictions and enhanced immunotherapies, and to the design of innovative strategies to reprogram the breast TME.
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Affiliation(s)
- Debaditya Chakraborty
- Department of Construction Science, The University of Texas at San Antonio, San Antonio, TX 78249, USA
| | - Cristina Ivan
- Department of Experimental Therapeutics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA; (C.I.); (P.A.); (C.R.-A.); (G.L.-B.)
- Center for RNA Interference and Non-Coding RNA, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA
| | - Paola Amero
- Department of Experimental Therapeutics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA; (C.I.); (P.A.); (C.R.-A.); (G.L.-B.)
| | - Maliha Khan
- Department of Lymphoma and Myeloma, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA;
| | - Cristian Rodriguez-Aguayo
- Department of Experimental Therapeutics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA; (C.I.); (P.A.); (C.R.-A.); (G.L.-B.)
- Center for RNA Interference and Non-Coding RNA, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA
| | | | - Gabriel Lopez-Berestein
- Department of Experimental Therapeutics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA; (C.I.); (P.A.); (C.R.-A.); (G.L.-B.)
- Center for RNA Interference and Non-Coding RNA, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA
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King D, Başağaoğlu H, Nguyen H, Healy F, Whitman M, Succi S. Effects of Advective-Diffusive Transport of Multiple Chemoattractants on Motility of Engineered Chemosensory Particles in Fluidic Environments. Entropy (Basel) 2019; 21:e21050465. [PMID: 33267179 PMCID: PMC7514954 DOI: 10.3390/e21050465] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 04/30/2019] [Accepted: 05/01/2019] [Indexed: 11/25/2022]
Abstract
Motility behavior of an engineered chemosensory particle (ECP) in fluidic environments is driven by its responses to chemical stimuli. One of the challenges to understanding such behaviors lies in tracking changes in chemical signal gradients of chemoattractants and ECP-fluid dynamics as the fluid is continuously disturbed by ECP motion. To address this challenge, we introduce a new multiscale numerical model to simulate chemotactic swimming of an ECP in confined fluidic environments by accounting for motility-induced disturbances in spatiotemporal chemoattractant distributions. The model accommodates advective-diffusive transport of unmixed chemoattractants, ECP-fluid hydrodynamics at the ECP-fluid interface, and spatiotemporal disturbances in the chemoattractant concentrations due to particle motion. Demonstrative simulations are presented with an ECP, mimicking Escherichia coli (E. coli) chemotaxis, released into initially quiescent fluids with different source configurations of the chemoattractants N-methyl-L-aspartate and L-serine. Simulations demonstrate that initial distributions and temporal evolution of chemoattractants and their release modes (instantaneous vs. continuous, point source vs. distributed) dictate time histories of chemotactic motility of an ECP. Chemotactic motility is shown to be largely determined by spatiotemporal variation in chemoattractant concentration gradients due to transient disturbances imposed by ECP-fluid hydrodynamics, an observation not captured in previous numerical studies that relied on static chemoattractant concentration fields.
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Affiliation(s)
- Danielle King
- Department of Mathematics, The University of Texas, Austin, TX 78712-1202, USA
- Correspondence:
| | - Hakan Başağaoğlu
- Mechanical Engineering Division, Southwest Research Institute, San Antonio, TX 78238-5166, USA
| | - Hoa Nguyen
- Department of Mathematics, Trinity University, One Trinity Place, San Antonio, TX 78212-7200, USA
| | - Frank Healy
- Department of Biology, Trinity University, One Trinity Place, San Antonio, TX 78212-7200, USA
| | - Melissa Whitman
- Department of Biology, Trinity University, One Trinity Place, San Antonio, TX 78212-7200, USA
| | - Sauro Succi
- Fondazione Istituto Italiano di Tecnologia, Center for Life Nanoscience at la Sapienza, vle Regina Margherita, 00165 Rome, Italy
- Istituto Applicazioni del Calcolo, Via dei Taurini 19, 00185 Roma, Italy
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Başağaoğlu H, Succi S, Wyrick D, Blount J. Particle Shape Influences Settling and Sorting Behavior in Microfluidic Domains. Sci Rep 2018; 8:8583. [PMID: 29872129 PMCID: PMC5988840 DOI: 10.1038/s41598-018-26786-7] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Accepted: 05/18/2018] [Indexed: 11/09/2022] Open
Abstract
We present a new numerical model to simulate settling trajectories of discretized individual or a mixture of particles of different geometrical shapes in a quiescent fluid and their flow trajectories in a flowing fluid. Simulations unveiled diverse particle settling trajectories as a function of their geometrical shape and density. The effects of the surface concavity of a boomerang particle and aspect ratio of a rectangular particle on the periodicity and amplitude of oscillations in their settling trajectories were numerically captured. Use of surrogate circular particles for settling or flowing of a mixture of non-circular particles were shown to miscalculate particle velocities by a factor of 0.9–2.2 and inaccurately determine the particles’ trajectories. In a microfluidic chamber with particles of different shapes and sizes, simulations showed that steady vortices do not necessarily always control particle entrapments, nor do larger particles get selectively and consistently entrapped in steady vortices. Strikingly, a change in the shape of large particles from circular to elliptical resulted in stronger entrapments of smaller circular particles, but enhanced outflows of larger particles, which could be an alternative microfluidics-based method for sorting and separation of particles of different sizes and shapes.
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Affiliation(s)
- Hakan Başağaoğlu
- Mechanical Engineering Division, Southwest Research Institute, San Antonio, TX, 78238, USA.
| | - Sauro Succi
- Istituto Applicazioni del Calcolo, via dei taurini 19, 00185, Roma, Italy
| | - Danielle Wyrick
- Space Science Division, Southwest Research Institute, San Antonio, TX, 78238, USA
| | - Justin Blount
- Defense Intelligence Solutions Division, Southwest Research Institute, San Antonio, TX, 78238, USA
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Camarillo MK, Loge FJ, Darby JL, Ginn TR, Başağaoğlu H, Foglia L. Modeling the inactivation of microorganisms occluded in effluent wastewater particles to enhance operation of filtration and disinfection systems. Water Environ Res 2011; 83:313-325. [PMID: 21553587 DOI: 10.2175/106143010x12681059116851] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In disinfection systems, incomplete penetration of chlorine into effluent wastewater particles can result in a residual population of viable microorganisms. In this work, a combined experimental and numerical approach was used to quantify inactivation of microorganisms in effluent particles and identify combinations of particle removal and chlorine dose that would result in a reduction of occluded microorganisms for six full-scale facilities in the United States with different nitrification levels. The results reveal that combined chlorine is more effective for inactivating occluded microorganisms than free chlorine; model calibration results suggest that free chlorine is less effective because it is more reactive. However, nitrified effluents appear to have lower effluent particle concentrations, and decreases in particle concentrations significantly reduce the chlorine required. Additionally, in disinfection systems that are designed and operated based on inactivation of indicator organisms, the chlorine dose may be insufficient to inactivate occluded pathogens to levels consistent with current regulations.
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Affiliation(s)
- Mary Kay Camarillo
- Department of Civil Engineering, University of the Pacific, Stockton, California 95211, USA.
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Başağaoğlu H, Succi S. Lattice-Boltzmann simulations of repulsive particle-particle and particle-wall interactions: Coughing and choking. J Chem Phys 2010; 132:134111. [DOI: 10.1063/1.3374685] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Loge FJ, Lambertini E, Borchardt MA, Başağaoğlu H, Ginn TR. Effects of etiological agent and bather shedding of pathogens on interpretation of epidemiological data used to establish recreational water quality standards. Risk Anal 2009; 29:257-266. [PMID: 19144071 DOI: 10.1111/j.1539-6924.2008.01184.x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
The overall goal of the study reported herein was to use techniques in the field of risk assessment (specifically a state-space population dynamic model of disease transmission within recreational waters) to explore the relative significance of (1) active shedding of microorganisms from bathers themselves, and (2) the type and concentration of etiological agent on the observed heterogeneity of the incidence of illness in epidemiological studies that have been used to develop ambient water quality criteria. The etiological agent and corresponding dose ingested during recreational contact was found to significantly impact the observed incidence of illness in an epidemiological study conducted in recreational water. In addition, the observed incidence of illness was found not to necessarily reflect background concentrations of indicator organisms, but rather microorganisms shed during recreational contact. Future revisions to ambient water quality criteria should address the etiological agent, dose, and the significance of microbial shedding relative to background concentrations of pathogens and indicator organisms in addition to the incidence of illness and concentration of indicator organisms. Without a quantitative assessment of these additional variables, study findings may potentially be site specific and not representative of the health risks associated with specific indicator concentrations in all recreational waters.
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Affiliation(s)
- Frank J Loge
- Department of Civil and Environmental Engineering, Universityof California Davis, Davis, CA 95616, USA.
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Abstract
Dewatered or "dry" grid cells in the USGS ground water modeling software MODFLOW may cause nonphysical artifacts, trigger convergence failures, or interfere with parameter estimation. These difficulties can be avoided in two dimensions by modifying the spatial differencing scheme and the iterative procedure used to resolve nonlinearities. Specifically, the spatial differencing scheme is modified to use the water level on the upstream side of a pair of adjacent cells to calculate the saturated thickness and hence intercell conductance for the pair. This makes it possible to explicitly constrain the water level in a cell to be at or above the cell bottom elevation without introducing nonphysical artifacts. Thus constrained, all initially active cells will remain active throughout the simulation. It was necessary to replace MODFLOW's Picard iteration method with the Newton-Raphson method to achieve convergence in demanding applications involving many dry cells. Tests using a MODFLOW variant based on the new method produced results nearly identical to conventional MODFLOW in situations where conventional MODFLOW converges. The new method is extremely robust and converged in scenarios where conventional MODFLOW failed to converge, such as when almost all cells dewatered. An example application to the Edwards Aquifer in south-central Texas further demonstrates the utility of the new method.
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Affiliation(s)
- Scott Painter
- Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238-5166, USA.
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Başağaoğlu H, Meakin P, Succi S, Redden GR, Ginn TR. Two-dimensional lattice Boltzmann simulation of colloid migration in rough-walled narrow flow channels. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 77:031405. [PMID: 18517379 DOI: 10.1103/physreve.77.031405] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2007] [Revised: 02/18/2008] [Indexed: 05/26/2023]
Abstract
A lattice Boltzmann model was used to simulate the accelerated transport of dense inert particles in low Reynolds number flows in smooth- and rough-walled narrow channels. The simulations showed that, after an initial transient, an initially immobile particle migrated faster than the average fluid velocity. The sensitivity of the particle residence time to wall roughness increased with decreasing Reynolds numbers. The relationship between the exit position and residence time of a particle was sensitive to the release position, flow strength, and the wall roughness. A particle with a density 5% larger than the density of the fluid migrated to an equilibrium position between the centerline and the wall for the slowest flow rates in rough-walled channels, displaying the Segre-Silberberg effect that a rigid neutrally buoyant spherical particle exhibits in small Reynolds number flows. However, a particle that was 35% denser than the density of the fluid drifted to the centerline in the slowest flows due to the gravitational settling effect. The difference in the residence time of the less-dense and dense particles was most sensitive to the surface roughness at the smallest Reynolds number investigated.
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Affiliation(s)
- H Başağaoğlu
- Department of Geosciences, Oregon State University, Corvallis, Oregon 97331, USA
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Dietrich JP, Loge FJ, Ginn TR, Başağaoğlu H. Inactivation of particle-associated microorganisms in wastewater disinfection: modeling of ozone and chlorine reactive diffusive transport in polydispersed suspensions. Water Res 2007; 41:2189-201. [PMID: 17389144 DOI: 10.1016/j.watres.2007.01.038] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2006] [Revised: 11/08/2006] [Accepted: 01/28/2007] [Indexed: 05/14/2023]
Abstract
Occlusion of microorganisms in wastewater particles often governs the overall performance of a disinfection system, and the associated health risks of post-disinfected effluents. Little is currently known on the penetration of chemical oxidants into particles developed in wastewater treatment. In this work, a reactive transport model that incorporates intra- and extra-particle chemical decay, radial intra-particle diffusion, mass transfer resistance at particle surfaces, and non-linear reaction kinetics within a competitive multi-particle size aqueous environment, was used to analyze the penetration of ozone and chlorine into wastewater particles. Individual characteristics from two secondary wastewater treatment facilities were used in model calibration. Simulations revealed that significant ozone transport within particles greater than 6 microm required large initial concentrations to exhaust the preferential reaction with aqueous soluble matter. Chlorinated samples exhibited apparently slower reactions and thus deeper penetration (22-40 microm). Chlorine penetration was less sensitive to variations in the extra-particle reaction and disinfectant concentration than ozone. Model simulations that considered elevated initial concentrations of chemical disinfectants revealed that complete inactivation of all particle size domains was not possible with current disinfection practices (e.g., contact times). Reduction in the health risks associated with wastewater particles requires treatment that efficiently balances particle removal (filtration) and particle inactivation (disinfection).
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Affiliation(s)
- Joseph P Dietrich
- Department of Civil and Environmental Engineering, University of California Davis, Davis, CA 95616, USA
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Başağaoğlu H, Meakin P, Succi S. Energy dissipation measures in three-dimensional disordered porous media. Phys Rev E Stat Nonlin Soft Matter Phys 2005; 72:046705. [PMID: 16383565 DOI: 10.1103/physreve.72.046705] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2005] [Indexed: 05/05/2023]
Abstract
The onset of nonlinear flow was analyzed in three-dimensional random, porous granular systems with 60% porosity using a lattice-Boltzmann model. Quantitative analysis was based on participation numbers built on local kinetic energies and energy dissipation rates computed via nonequilibrium kinetic (viscous stress) tensors. In contrast to the kinetic energy participation number, which characterizes the onset of nonlinearity in terms of a transition from a locally concentrated to a dispersed distribution of kinetic energy densities, the nonequilibrium kinetic tensor participation number characterizes the onset of nonlinearity in terms of a transition from a dispersed to a locally concentrated distribution of energy dissipation densities as the flow rate increases. The transition characterized by the nonequilibrium kinetic tensor participation number occurred over a nearly equal or a narrower range of Reynolds numbers when compared to the transition characterized by the kinetic energy participation number.
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Affiliation(s)
- H Başağaoğlu
- Idaho National Laboratory, P.O. Box 1625, MS 2025, Idaho Falls, Idaho 83415, USA
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Abstract
A two-dimensional lattice-Boltzmann model (LBM) with fluid-fluid interactions was used to simulate first-order phase separation in a thin fluid film. The intermediate asymptotic time dependence of the mean island size, island number concentration, and polydispersity were determined and compared with the predictions of the distribution-kinetics model. The comparison revealed that the combined effects of growth, coalescence, and Ostwald ripening control the phase transition process in the LBM simulations. However, the overall process is dominated by coalescence, which is independent of island mass. As the phase transition advances, the mean island size increases, the number of islands decrease, and the polydispersity approaches unity, which conforms to the predictions of the distribution-kinetics model. The effects of the domain size on the intermediate asymptotic island size distribution, scaling form of the island size distribution, and the crossover to the long-term asymptotic behavior were elucidated.
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Affiliation(s)
- Hakan Başağaoğlu
- Idaho National Engineering and Environmental Laboratory, Idaho Falls, ID 83415-2025, USA
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Dietrich JP, Başağaoğlu H, Loge FJ, Ginn TR. Preliminary assessment of transport processes influencing the penetration of chlorine into wastewater particles and the subsequent inactivation of particle-associated organisms. Water Res 2003; 37:139-149. [PMID: 12465795 DOI: 10.1016/s0043-1354(02)00239-7] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The diffusion of a chemical disinfectant into wastewater particles may be viewed as a serial two-step process involving transport through a macroporous network of pathways to micropores that lead into dense cellular regions. Previous research reveals that ultraviolet (UV) light penetration into wastewater particles is limited primarily to macropores, resulting in a residual concentration of targeted organisms in post-disinfected effluents that reflects the number of organisms embedded in the dense cellular regions of particles. Conversely, chlorine was demonstrated as part of this research to penetrate into both the macroporous and microporous network of pathways, implying that the application of chlorine may be designed feasibly to achieve a desired level of inactivation of particle-associated organisms. In the short term, a disinfection model previously developed for UV irradiation may be used to assess the inactivation of particle-associated organisms with chlorine. However, in the long-term, a more rigorous and complete understanding of the transport of chemical disinfectants into particles can be explored utilizing existing mathematical expressions commonly used to model mass transport into porous media. The parameters of interest in this modeling approach include the reaction rate of chlorine with particulate material, the diffusion rate of chlorine within a particle, the mass-transfer rate coefficient across the particle's boundary, and the particle porosity.
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Affiliation(s)
- Joseph P Dietrich
- Department of Civil and Environmental Engineering, Washington State University, P.O. Box 642910, Pullman, WA 99164-2910, USA
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Abstract
A semianalytical soil-pesticide transport model is formulated based on a compartmental approach to determine spatial and temporal variations of pesticide residues across a soil profile. The compartmental model is implemented by drawing an analogy between a series of continuous-flow stirred tank reactors and a soil horizon that consists of multiple perfectly mixed compartments. The analogy is strengthened by exploiting a relation between the compartment series and the conventional convective-dispersive equation (CDE) for vertical transport in the soil. Consequently, the number of compartments in the model formulation is not free, but dictated as a function of transport parameters. The model formulation allows consideration of arbitrary boundary value specifications and also, for some cases, spatially varying initial concentration profiles. Sorption kinetics is represented via a two-site model that involves a linear sorption isotherm and a first-order irreversible sorption or a radial diffusive penetrating model. For these three cases, analysis of the compartmental model allows the resultant concentration profiles to be expressed in terms of the Poisson distribution. When a nonlinear kinetic sorption model is used to simulate the sorption processes, an analytical solution is not found and a numerical approach is required.
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Affiliation(s)
- Hakan Başağaoğlu
- Department of Civil and Environmental Engineering, University of California, Davis 95616, USA.
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