Filtration Model Research Articles

NIMG-47. MULTI-INSTITUTIONAL VALIDATION OF AN AI-BASED MODEL FOR PREDICTION OF TUMOR INFILTRATION AND FUTURE RECURRENCE IN PATIENTS WITH GLIOBLASTOMA: RESULTS FROM THE RESPOND CONSORTIUM

Abstract BACKGROUND Glioblastoma is an infiltrative primary brain tumor with poor prognosis despite multimodal therapy. Recurrence is inevitable secondary to tumor cell infiltration in the peritumoral tissues, beyond contrast enhancing margins, which is the target for surgical resection. We hypothesize that a machine learning model constructed from a diverse, inter-institutional dataset can improve accuracy of generated tumor infiltration maps, thus guiding precision targeted therapies. METHODS 731 MRI scans of treatment-naïve glioblastoma patients from 10 institutions were included. All patients had pre-operative multiparametric-MRI (T1, T1Gd, T2, T2-FLAIR, ADC), and underwent complete resection of the enhancing tumor followed by standard-of-care chemoradiotherapy. 42 patients were used as an independent validation set, and 689 were used for training. Of these 239 patients had histopathologically confirmed recurrence with corresponding MRI scans, which were used as ground-truth for evaluating the location of recurrence using a leave-one-site-out (LSO) method. An AI model combining deep learning and SVM was used to develop a predictive model for infiltration. We validated the generalizability of our results in an unseen, multi-institutional data set. RESULTS Our model predicted locations of recurrence with odds ratio (99% CI) 37.6 (37.1-38.1) on the LSO testing set and 24.3 (23.4-25.2) on the validation set, indicating that areas labeled highly infiltrated were over 37 and 24 times more likely to coincide with future recurrence respectively. CONCLUSIONS We demonstrate that AI-based pattern analysis from multiparametric-MRI can predict tumor infiltration in peritumoral regions with high likelihood of recurrence by decrypting the visually imperceptible heterogeneity of peritumoral tissue. Model performance improved from training on a larger/diverse dataset and combining results of multiple AI methods. Independent validation confirmed the model’s ability to generalize to unseen data. We believe this will serve to advance AI-based biomarkers for predicting future recurrence and facilitate development of multi-modal targeted therapies in this era of precision neuro-oncology.

Unveiling Tim-3 immune checkpoint expression in hepatocellular carcinoma through abdominal contrast-enhanced CT habitat radiomics

IntroductionImmune checkpoint inhibitors (ICIs) are important systemic therapeutic agents for hepatocellular carcinoma (HCC), among which T-cell immunoglobulin and mucin-domain containing protein 3 (Tim-3) is considered an emerging target for ICI therapy. This study aims to evaluate the prognostic value of Tim-3 expression and develop a predictive model for Tim-3 infiltration in HCC.MethodsWe collected data from 424 HCC patients in The Cancer Genome Atlas (TCGA) and data from 102 pathologically confirmed HCC patients from our center for prognostic analysis. Multivariate Cox regression analyses were performed on both datasets to determine the prognostic significance of Tim-3 expression. In radiomics analysis, we used the K-means algorithm to cluster regions of interest in arterial phase enhancement and venous phase enhancement images from patients at our center. Radiomic features were extracted from three subregions as well as the entire tumor using pyradiomics. Five machine learning methods were employed to construct Habitat models based on habitat features and Rad models based on traditional radiomic features. The predictive performance of the models was compared using ROC curves, DCA curves, and calibration curves.ResultsMultivariate Cox analyses from both our center and the TCGA database indicated that high Tim-3 expression is an independent risk factor for poor prognosis in HCC patients. Higher levels of Tim-3 expression were significantly associated with worse prognosis. Among the ten models evaluated, the Habitat model constructed using the LightGBM algorithm showed the best performance in predicting Tim-3 expression status (training set vs. test set AUC 0.866 vs. 0.824).DiscussionThis study confirmed the importance of Tim-3 as a prognostic marker in HCC. The habitat radiomics model we developed effectively predicted intratumoral Tim-3 infiltration, providing valuable insights for the evaluation of ICI therapy in HCC patients.

Intermittent Drip Irrigation Soil Wet Front Prediction Model and Effective Water Storage Analysis

The depth and width of drip infiltration play a critical role in designing effective irrigation strategies. However, existing models primarily focus on continuous irrigation and fail to predict wetting patterns under intermittent drip irrigation. This study developed an infiltration model to estimate soil moisture depth and width under intermittent drip irrigation and identified strategies that enhance effective water storage. Indoor soil box simulations were conducted, with continuous drip irrigation as the control. Results showed that intermittent irrigation increased infiltration width and reduced depth, maximizing water storage efficiency. We recommend adopting an intermittent irrigation system with 1.5 h of irrigation followed by a 0.5 h interval, repeated four times. This system increased effective water storage by up to 16.23% compared to continuous irrigation. The proposed method is suitable for sandy loam farmland in southern Xinjiang and can significantly improve water use efficiency in arid regions.

Parameterizing Haverkamp Model From the Steady‐State of Numerically Generated Infiltration: Influence of Algorithms for Steady‐State Selection

ABSTRACTBEST (Beerkan Estimation of Soil Transfer parameters) methods of soil hydraulic characterisation are widely applied for estimating sorptivity, S, and saturated hydraulic conductivity, Ks. Calculating these properties requires choosing the β and γ parameters of the Haverkamp infiltration model. These parameters can be obtained from numerically simulated three‐dimensional (3D) infiltration runs reaching steady‐state. This investigation tested dependence of the estimated β and γ parameters on the algorithm for steady‐state selection using simulated 3D cumulative infiltrations for different soils and initial conditions. Two algorithms used the original simulation outputs and included using (i) a threshold defining steadiness (T‐algorithm) and (ii) the last four data points, yielding a reference value of steady‐state infiltration rate (R‐algorithm). A third algorithm, similar to the R‐algorithm, was applied to previously re‐sampled infiltration data at fixed time intervals (RR‐algorithm). The intercept, bs, of the straight line fitted to the data describing steady‐state on the cumulative infiltration plot depended on the applied algorithm more than the slope of this line. Consequently, β varied with the applied algorithm more than γ. The RR‐algorithm, yielding 0.62 ≤ β ≤ 1.99 and 0.74 ≤ γ ≤ 0.98, was preferred since it mediated between advantages and disadvantages of T‐ and R‐algorithms. The influence of the choice of proper values for β and γ on the estimates of S and Ks was evaluated using BEST. Using the default values of β (0.6) and γ (0.75) yielded accurate estimates of S but not of Ks. Soil dependent β and γ values should be used in this case. A check of the reliability of the estimates of bs can be made by a sequential analysis of the cumulative infiltration data. Future developments include considering sources differing in size and establishing if the suggested β and γ values apply in general to the available BEST algorithms.

Numerical Modeling of Two-Phase Fluid Filtration for Carbonate Reservoir in Two-Dimensional Formulation

This work considers the isothermal process of incompressible viscous fluid filtration in an oil-saturated, fractured-porous reservoir. A study of the pressure and water saturation distribution process is carried out for a case in which a production well is put into operation. For this problem, i.e., a mathematical model in a two-dimensional formulation, a numerical method and a parallel algorithm are proposed. The mathematical model of two-phase filtration is written in accordance with the classical laws of continuum mechanics and Darcy’s law and also includes a function of fluid exchange between low-permeability pores and high-permeability natural fractures within the framework of the Warren–Root model. The numerical solution is based on the finite-difference method and a splitting scheme of physical processes and spatial coordinates. For a split system with respect to piezoconductivity, an implicit finite-difference scheme with fixed saturations is constructed, and with respect to saturation transfer, explicit and implicit difference schemes are constructed. For parallel implementation of the developed numerical approach, a method based on geometric parallelism is selected. Testing of the developed method is performed using the example of calculating liquid mass transfer for a wide range of parameters. To verify the model, the obtained calculated pressure curves are compared with field data recorded by a deep-well measuring device. The results allow for estimation of the distribution of reservoir pressure and water saturation depending on the permeability of the fracture set and the pore part. The obtained results allow for monitoring of well operations, reducing unexpected accident risks and optimizing the development system in order to increase oil production in fractured-porous reservoirs. Computational experiments confirm the efficiency of the developed numerical algorithm and its parallel implementation.

Solution of the problem with a small parameter in suspension filtration in a porous medium

Relevance. The necessity to calculate the changes in filtration properties during injection of suspensions for subsequent forecasting of technological parameters of wells. This calculation is complicated by the presence of different-scale effects, since the penetration depth of dispersed particles is orders of magnitude smaller than the characteristic dimensions of the formation. These effects have not been studied in detail before. Aim. To analyze the effect of a small parameter on the behavior of flow characteristics using a mathematical model of suspension filtration in a porous medium. Objects. Colmatation coefficient, filtration coefficient, distribution of concentration of dispersed particles in the formation, porosity, mathematical model of deep-bed suspension migration into a porous medium. Methods. Numerical modeling, explicit finite-difference scheme, solution of a problem with a small parameter, introduction of dimensionless parameters, method of characteristics. Results and conclusions. It is shown that the processes of conformance control and colmatation of a porous medium are described within the framework of a unified system of equations of deep-bed suspension migration into a porous medium. It is identified that the concentration of retained particles is a small parameter that allows reducing the complete system of equations of deep-bed suspension migration into a porous medium to a simplified form, in which the solution can be obtained analytically using the method of characteristics. The authors compared the solutions of the complete and simplified systems of equations of deep-bed suspension migration into a porous medium, indicating their compliance with an error of less than 4 %. They obtained the distributions of the concentration of dispersed particles and porosity in the reservoir during colmatation, showing that over time the colmatation front propagates at a constant rate. It is shown that the colmatation coefficient is a small parameter that significantly determines the nature of oil displacement by water, and a decrease in the colmatation coefficient leads to a decrease in the rate of colmatation and the appearance and growth of the size of the stabilized zone near the displacement front.

Numerical Method for the Variable-Order Fractional Filtration Equation in Heterogeneous Media

This paper presents a study of the application of the finite element method for solving a fractional differential filtration problem in heterogeneous fractured porous media with variable orders of fractional derivatives. A numerical method for the initial-boundary value problem was constructed, and a theoretical study of the stability and convergence of the method was carried out using the method of a priori estimates. The results were confirmed through a comparative analysis of the empirical and theoretical orders of convergence based on computational experiments. Furthermore, we analyzed the effect of variable-order functions of fractional derivatives on the process of fluid flow in a heterogeneous medium, presenting new practical results in the field of modeling the fluid flow in complex media. This work is an important contribution to the numerical modeling of filtration in porous media with variable orders of fractional derivatives and may be useful for specialists in the field of hydrogeology, the oil and gas industry, and other related fields.

Applying a Comprehensive Model for Single-Ring Infiltration: Assessment of Temporal Changes in Saturated Hydraulic Conductivity and Physical Soil Properties

Modeling agricultural systems, from the point of view of saving and optimizing water, is a challenging task, because it may require multiple soil physical and hydraulic measurements to investigate the entire crop cycle. The Beerkan method was proposed as a quick and easy approach to estimate the saturated soil hydraulic conductivity, Ks. In this study, a new complete three-dimensional model for Beerkan experiments recently proposed was used. It consists of thirteen different calculation approaches that differ in estimating the macroscopic capillary length, initial (θi) and saturated (θs) soil water contents, use transient or steady-state infiltration data, and different fitting methods to transient data. A steady-state version of the simplified method based on a Beerkan infiltration run (SSBI) was used as the benchmark. Measurements were carried out on five sampling dates during a single growing season (from November to June) in a long-term experiment in which two soil management systems were compared, i.e., minimum tillage (MT) and no tillage (NT). The objectives of this work were (i) to test the proposed new model and calculation approaches under real field conditions, (ii) investigate the impact of MT and NT on soil properties, and (iii) obtain information on the seasonal variability of Ks and other main soil physical properties (θi, soil bulk density, ρb, and water retention curve) under MT and NT. The results showed that the model always overestimated Ks compared to SSBI. Indeed, the estimated Ks differed by a factor of 11 when the most data demanding (A1) approach was considered by a factor of 4–8, depending on the transient or steady-state phase use, when A3 was considered and by a practically negligible factor of 1.0–1.9 with A4. A relatively higher seasonal variability was detected for θi at the MT than NT system. Under both MT and NT, ρb did not change between November and April but increased significantly until the end of the season. The selected calculation approaches provided substantially coherent information on Ks seasonal evolution. Regardless of the approach, the results showed a temporal stability of Ks at least from early April to June under NT; conversely, the MT system was, overall, more affected by temporal changes with a relative stability at the beginning and middle of the season. These findings suggest that a common sampling time for determining Ks could be set at early spring. Soil management affected the soil properties, because the NT system was significantly wetter and more compact than MT on four out of five dates. However, only NT showed a significantly increasing correlation between Ks and the modal pore diameter, suggesting the presence of a relatively smaller and better interconnected pore network in the no-tilled soil. This study confirms the need to test infiltration models under real field conditions to evaluate their pros and cons. The Beerkan method was effective for intensive soil sampling and accurate field investigations on the temporal variability of Ks.

Application of tracer studies results for adaptation of hydrodynamic models of oil fields

To date, a large array of tracer results has been accumulated, which are mainly processed analytically without further use in numerical hydrodynamic modelling, despite the fact that most commercial hydrodynamic simulators have modules for tracer modelling, which is undoubtedly an omission. Using the results of tracer studies makes it possible to select a filtration model, to specify both filtration-capacitance properties of productive sediments of the interwell space and the type of void space, which can serve as valuable factual material for analyses and development design.

Applications of coagulation-sedimentation and ultrafiltration for the removal of nanoparticles from water

The removal of engineered nanoparticles (NPs) in drinking water treatment has posed a longstanding challenge due to their small sizes and widespread presence. This study aimed to assess the effectiveness of different methods, namely natural sedimentation, coagulation-sedimentation, and polyvinyl chloride (PVC) membrane ultrafiltration (UF), in removing silver NPs coated with carboxyl-terminated polymer with a primary diameter of 4.7 nm, hematite NPs of three diameters (53, 98, and 205 nm), and SiO2 NPs (740 nm). The results revealed that after 24 h of natural sedimentation, only approximately 28 %, 10 %, and 3 % of SiO2, hematite, and silver NPs, respectively, were removed. However, when coagulation with aluminum sulphate at an Al3+ dosage of 60 mg/L was implemented, followed by 4 h of sedimentation, the removal efficiencies of the three types of NPs increased to 90–95 %. Furthermore, membrane ultrafiltration achieved removal rates of 99.95 % for hematite, 99.6 % for silver, and 99.70 % for SiO2, unaffected by variations in solution pH (ranging from 5.0 to 10.0) and the initial concentrations (approximately 10 and 100 mg/L). Analyses based on the blocking filtration model indicated that the primary removal mechanism involved straining for 53 nm-hematite NPs, and a combination of straining and inside pore attachment for silver NPs.

Implicit EXP-RBF techniques for modeling unsaturated flow through soils with water uptake by plant roots

Modeling unsaturated flow through soils with water uptake by plan root has many applications in agriculture and water resources management. In this study, our aim is to develop efficient numerical techniques for solving the Richards equation with a sink term due to plant root water uptake. The Feddes model is used for water absorption by plant roots, and the van-Genuchten model is employed for capillary pressure. We introduce a numerical approach that combines the localized exponential radial basis function (EXP-RBF) method for space and the second-order backward differentiation formula (BDF2) for temporal discretization. The localized RBF methods eliminate the need for mesh generation and avoid ill-conditioning problems. This approach yields a sparse matrix for the global system, optimizing memory usage and computational time. The proposed implicit EXP-RBF techniques have advantages in terms of accuracy and computational efficiency thanks to the use of BDF2 and the localized RBF method. Modified Picards iteration method for the mixed form of the Richards equation is employed to linearize the system. Various numerical experiments are conducted to validate the proposed numerical model of infiltration with plant root water absorption. The obtained results conclusively demonstrate the effectiveness of the proposed numerical model in accurately predicting soil moisture dynamics under water uptake by plant roots. The proposed numerical techniques can be incorporated in the numerical models where unsaturated flows and water uptake by plant roots are involved such as in hydrology, agriculture, and water management.

Deep Infiltration Model to Quantify Water Use Efficiency of Center-Pivot Irrigated Alfalfa

Deep Infiltration Model to Quantify Water Use Efficiency of Center-Pivot Irrigated Alfalfa

Selected applications of satellite technologies in rail transport

Global Navigation Satellite Systems (GNSS) are increasingly being used in various modes of transport, including rail transport. When this technology is applied to railway traffic control, it is essential to ensure a high level of safety and reliability. The approval of a railway traffic control system requires a safety analysis, which includes hazard analysis and risk analysis. This also includes GNSS-based solutions in terms of their compliance with safety integrity requirements, i.e. THR (Tolerable Hazard Rate) and SIL (Safety Integrity Level) parameters, as defined in normative documents. In the case of railway traffic control systems, the level of dependability of the determined train position, referred to as position integrity, is very important in ensuring safety. Position integrity is affected by many factors, including: errors due to SIS (Signal-In-Space) propagation, multipath errors, signal interference or GNSS receiver errors. In order to improve position integrity, among other things, new data processing methods can be used to improve the accuracy and reliability of measurements. The paper presents the concept of satellite signal processing for precise determination of the position of objects in selected railway systems. The Kalman filter based model of satellite signal filtration and its selected applications, which were tested in the real condition, was presented. The application of Kalman filtration indicated in the paper is a universal method that improves the estimated measurement parameters and can be used in many applications of satellite systems for railway tasks. The applicability of satellite systems to automatic train operation, defect positioning in automatic and manual flaw detection tests, determining track spatial orientation and train integrity control have been considered. The conducted tests confirmed the correctness of the adopted concept and the model of satellite signals filtration developed for this purpose. According to the authors, the described methods can also be used in many other tasks related to rail transport.

STUDY OF PHYSICOCHEMICAL AND BIOLOGICAL PROPERTIES OF A NEW BISPIDINE WITH A MORPHOLINE FRAGMENT

The experimental results obtained during the work enrich modern medicinal chemistry with new information about the development and local anesthetic activity of a promising class of chemical compound - O-benzoyloxime of bispidine. The discovered new properties of the molecule can serve as the basis for the creation of a new domestic safe local anesthetic drug that is effective in models of infiltration and conduction anesthesia and has low toxicity. The aim of this work is to synthesize and study the physicochemical and biological properties of a new morpholino-substituted bispidine derivative. Results and discussion. 3-(3-(Ethan-1-yloxy)propyl)-7-[3-(morpholine-4-yl)propyl]-3,7-diazabicyclo[3.3.1]nonan-9-one was constructed in 56.9% yield. Oximation under the influence of a powerful oximylating agent led to the oxime. O-Benzoyloxime was synthesized by benzoylation of the oxime. The complex of O-benzoyloxime with β-cyclodextrin - LA-180 was studied for local anesthetic activity and acute toxicity. Conclusion. It was established that LA-180 manifested itself as a highly active compound in a series of experiments studying infiltration and conduction anesthesia. The results of a study of acute toxicity after a single subcutaneous administration to white outbred mice showed that LA-180 (925 mg/kg) is a low-toxic compound in comparison with standard drugs such as trimecaine, lidocaine and novocaine.

Evaluation of infiltration models based on simple multicriteria decision making across various soil types and land uses in India

Evaluation of infiltration models based on simple multicriteria decision making across various soil types and land uses in India

Modeling of Filtration and Heat and Mass Transfer Processes in Groundwater

Purpose. The method of mathematical modeling is an important tool for solving complex problems involving the analysis of groundwater dynamics and heat and mass transfer processes in them when studying their contamination from various anthropogenic sources in the event of accidental spills of chemically hazardous substances, etc. The main purpose of the article is to develop a set of mathematical models for calculating the process of filtration of non-pressure groundwater, mass transfer of impurities and the process of heat transfer in groundwater. Methodology. The two-dimensional Boussinesq equation of filtration was used to predict the dynamics of groundwater. The two-dimensional equation of convective-diffusive transport of impurities was used to model the processes of mass transfer in groundwater. The process of freezing of individual sections of the groundwater flow is modeled using the Laplace equation for the velocity potential (calculation of the flow velocity field in a time-varying geometry) and the two-dimensional equation of heat transfer in groundwater. Finite difference schemes were used to solve the modeling equations of groundwater dynamics and heat and mass transfer. Findings. A set of mathematical models has been developed to calculate the process of filtration of non-pressure groundwater and its chemical contamination. The experiment has confirmed the adequacy of the constructed numerical model of filtration of a non-pressure groundwater flow. An effective mathematical model was developed that allows determining the temperature fields in groundwater during the operation of a well used to freeze certain sections of the flow. The results of computer modeling indicate the effectiveness of the developed mathematical models. Originality. Effective mathematical models for predicting the level of chemical contamination of groundwater, its dynamics and thermal regime are proposed. The constructed mathematical models make it possible to determine the dynamics of changes in the temperature regime of groundwater during the operation of wells through which refrigerant is supplied to freeze individual areas. A computer program has been developed that allows for a comprehensive assessment of groundwater conditions. Practical value. A set of computer programs has been developed to conduct a computational experiment to study the processes of filtration, chemical contamination of groundwater and heat transfer processes in them. This set of programs can be used for the scientific substantiation of engineering solutions aimed at protecting groundwater.

Assessing the performance of various infiltration models to improve water management practices

AbstractInfiltration plays a key role in stormwater management and irrigation scheduling. A review of previous studies reveals that the effectiveness of infiltration models varies significantly depending on soil characteristics and field conditions. Accurate predictions depend on selecting appropriate models for specific sites because of soil spatial variability. This requires extensive testing and recording of infiltration rates at each location. This study assesses various infiltration rate measurement models to enhance water management efficiency. Infiltration rate measurements were conducted at three sites in Dehradun using a double-ring infiltrometer. Well-established models, such as Philips JR, Green, Ampt, Horton, Kostiakov, modified Kostiakov, and the Soil Conservation Service (SCS) model, were evaluated. Data from infiltration tests were used to calibrate these models, facilitating better irrigation system design and stormwater management. In assessing their effectiveness and efficiency, key evaluation criteria such as Nash–Sutcliffe efficiency (NSE), R-squared (R2), root mean square error (RMSE), mean absolute error (MAE), and mean bias error (MBE) were employed. Our findings highlight the superiority of the Philips JR model, offering the highest overall accuracy with the highest average value R2 = 0.9557 and NSE = 0.9553, lowest MAE = 0.6717 cm/h, MBE = − 0.0160 cm/h and RMSE = 1.0077 cm/h. These results underscore the model’s ability to synthesize infiltration data effectively, even in the absence of direct measurements. This insight positions the Philips JR model as a valuable tool for estimating infiltration rates in similar conditions.

Numerical modelling of CMAS infiltration and dimensionless numbers of anti-infiltration designs of thermal barrier coatings

Resistance to calcium–magnesium–alumina–silicate (CMAS) infiltration and corrosion is a crucial problem for safely applying thermal barrier coatings (TBCs) in advanced aero engines. This work proposes a CMAS infiltration model based on the phase-field method to simulate the CMAS infiltration process in TBCs and analyse the influence factor. Further, a key dimensionless number called relative driving force K=rσcos(θc)tsμϛ2hTC2 was found to determine the CMAS infiltration depth using dimensional analysis. A criterion of K<2 was derived and was considered to be the evaluation standard of TBCs with excellent CMAS infiltration resistance. Based on K minimization, novelty TBCs with microstructure of S-shaped intercolumnar gaps and spherical pores are expected to significantly improve the resistance to CMAS infiltration and corrosion.

Non-linear filtration model with splitting front

We consider filtration of a suspension in a homogeneous porous medium which is described by a macroscopic 1-D model including the mass exchange equation and the kinetic equation for deposit growth. The standard model assumes that suspended particles move at the same speed as the carrier fluid. However, in some experiments, a lag between the front boundary of suspended particles and the front of the carrier fluid was observed. This article proposes a modification of the standard model that provides a description of the separation between the fluid front and the particle front. For this purpose, a non-smooth non-linear function depending on the concentration of the suspension is introduced into the deposit growth equation. In case of a non-smooth suspension function, the concentration of suspended particles at the front decreases to zero in a finite time. At this moment the united front splits into the front of pure injected water and the front of suspended and retained particles. The particle front moves slower than the pure water front. In case of a linear filtration function (Langmuir coefficient), an exact solution is constructed in a closed form. For the filtration problem with a suspension function in the form of a square root, explicit analytical formulae are obtained. In case of a non-smooth filtration function, the filtration time is finite. The curvilinear boundary separates the filtration domain, where concentrations increase with time, from the stabilization domain, where the concentrations of suspended and retained particles have reached their limits. The limit speeds of the stabilization border and of the particle front coincide.

Sedimentation of heterogeneous particles in a porous material

Filtration of suspensions and colloids in porous materials occurs during the construction and operation of hydraulic structures, tunnels and underground storage facilities. Filtration models are used to calculate the penetration of grout into loose soil, when treating drinking water and industrial wastewater. During the filtration process, suspended particles pass through large pores and get stuck at the entrance of small-diameter pores. The trapped particles form a stationary deposit. A model of filtration of a polydisperse suspension in a porous material is considered. The purpose of the work is to study sediment profiles – the dependence of the concentration of deposited particles on the distance to the porous material inlet at a fixed time. An exact solution to the model was constructed using the method of characteristics. It has been shown that when filtering a polydisperse suspension, the distribution of sediment differs for different types of particles. The sediment profile of the largest particles always decreases monotonically, but the sediment profile of the smallest particles is not monotonic. It decreases at short times, then a maximum point appears on the graph, moving along the porous medium as time increases. After the maximum point reaches the porous material exit, the sediment profile becomes monotonically increasing. The sediment profiles of intermediate size particles and the total sediment profile are either monotonic or non-monotonic depending on the model parameters. The behavior of maximum points of non-monotonic profiles has been studied.