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Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater.

ABSTRACT: The study presents a meshless computational approach for simulating the three-dimensional multi-term time-fractional mobile-immobile diffusion equation in the Caputo sense. The methodology combines a stable Crank-Nicolson time-integration scheme with the definition of the Caputo derivative to discretize the problem in the temporal direction. The spatial function derivative is approximated using the inverse multiquadric radial basis function. The solution is approximated on a set of scattered or uniform nodes, resulting in a sparse and well-conditioned coefficient matrix. The study highlights the advantages of meshless method, particularly their simplicity of implementation in higher dimensions. To validate the accuracy and efficacy of the proposed method, we performed numerical simulations and compared them with analytical solutions for various test problems. These simulations were carried out on computational domains of both rectangular and non-rectangular shapes. The research highlights the potential of meshless techniques in solving complex diffusion problems and its successful applications in groundwater contamination and other relevant fields.

SUBMITTER: Ahmad I

PROVIDER: S-EPMC10707926 | biostudies-literature | 2023

REPOSITORIES: biostudies-literature

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Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater.

Ahmad Imtiaz I Ali Ihteram I Jan Rashid R Idris Sahar Ahmed SA Mousa Mohamed M

PloS one 20231208 12

The study presents a meshless computational approach for simulating the three-dimensional multi-term time-fractional mobile-immobile diffusion equation in the Caputo sense. The methodology combines a stable Crank-Nicolson time-integration scheme with the definition of the Caputo derivative to discretize the problem in the temporal direction. The spatial function derivative is approximated using the inverse multiquadric radial basis function. The solution is approximated on a set of scattered or ...[more]

PMID: 38064451

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Project description:BACKGROUND AND OBJECTIVES:The inflammation-driven increase in peritoneal solute transport rate that occurs during long-term peritoneal dialysis is associated with higher mortality, hospitalization, and encapsulating peritoneal sclerosis. Because biocompatible solutions were developed to mitigate these effects, we examined the association with their use and longitudinal peritoneal solute transport rate. DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS:We analyzed subjects from the multinational prospective Global Fluid Study with three or more peritoneal solute transport rate measurements >2 months from the start of peritoneal dialysis. Follow-up was for 7.5 years (median, 2.3 years; interquartile range, 1.8-3.6) in biocompatible solutions and 12.8 years (median, 3.2 years; interquartile range, 1.9-4.3) for standard solutions. Using a random intercept/slopes multilevel model, we examined the association of patients using biocompatible solutions and peritoneal solute transport rate over time, adjusting for center effects, dialysate dextrose concentration, baseline dialysate IL-6 concentration, icodextrin use, residual kidney function, and peritonitis. RESULTS:Of 366 patients, the 71 receiving biocompatible solutions throughout their time on peritoneal dialysis had a mean adjusted dialysate-to-plasma creatinine ratio of 0.67 compared with 0.72 for standard solutions (P=0.02). With duration of treatment, there was a continuous increase in peritoneal solute transport rate in patients using standard solutions (range, 2 months to 4 years). In contrast, patients using biocompatible solutions had peritoneal solute transport rates that plateaued after 2 years of therapy. These changes in peritoneal solute transport rate were independent of baseline inflammation and time-varying predictors of faster peritoneal solute transport rate. In patients suffering episodes of peritonitis while using standard solutions, there was an associated increase in peritoneal solute transport rate of 0.020 (95% confidence interval, 0.01 to 0.03) per episode, whereas in patients using biocompatible solutions, there was no change in this parameter (-0.014; 95% confidence interval, -0.03 to <0.01). CONCLUSIONS:These data suggest that a different temporal pattern in changes in peritoneal solute transport rate occurs during the course of peritoneal dialysis according to solution type and that patients using biocompatible solutions may avoid the increase in solute transport associated with peritonitis.

Project description:Background Three-dimensional (3D) fractional moving blood volume (FMBV) derived from 3D power Doppler US has been proposed for noninvasive approximation of perfusion. However, 3D FMBV has never been applied in animals against a ground truth. Purpose To determine the correlation between 3D FMBV and the reference standard of fluorescent microspheres (FMS) for measurement of renal perfusion in a porcine model. Materials and Methods From February 2017 to September 2017, adult pigs were administered FMS before and after measurement of renal 3D FMBV at baseline (100%) and approximately 75%, 50%, and 25% flow levels by using US machines from two different vendors. The 3D power Doppler US volumes were converted and segmented, and correlations between FMS and 3D FMBV were made with simple linear regression (r2). Similarity and reproducibility of manual segmentation were determined with the Dice similarity coefficient and 3D FMBV reproducibility (intraclass correlation coefficient [ICC]). Results Thirteen pigs were studied with 33 flow measurements. Kidney volume (mean Dice similarity coefficient ± standard deviation, 0.89 ± 0.01) and renal segmentation (coefficient of variation = 12.6%; ICC = 0.86) were consistent. The 3D FMBV calculations had high reproducibility (ICC = 0.97; 95% confidence interval: 0.96, 0.98). The 3D FMBV per-pig correlation showed excellent correlation for US machines from both vendors (mean r2 = 0.96 [range, 0.92-1.0] and 0.93 [range, 0.78-1.0], respectively). The correlation between 3D FMBV and perfusion measured with microspheres was high for both US machines (r2 = 0.80 [P < .001] and 0.70 [P < .001], respectively). Conclusion The strong correlation between three-dimensional (3D) fractional moving blood volume (FMBV) and fluorescent microspheres indicates that 3D FMBV shows excellent correlation to perfusion and good reproducibility. © RSNA, 2019 Online supplemental material is available for this article. See also the editorial by Morrell et al in this issue.

Dataset Information

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater.

Publications

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater.

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