Mathematical Model Research Articles

In Silico Design of Novel Piperazine-Based mTORC1 Inhibitors Through DFT, QSAR and ADME Investigations

Mammalian target of rapamycin complex 1 (mTORC1) is an important and promising alternative biological target for the treatment of different types of cancer including breast, lung and renal cell carcinoma. This study contributed to the development of mathematical models highlighting the quantitative structure-activity relationship of a series of piperazine derivatives reported as mTORC1 inhibitors. Various molecular descriptors were calculated using Gaussian 09, Chemsketch, and ChemOffice software. The density funcional theory (DFT) method at the level B3LYP/6-31G+(d, p) was applied to determine the structural, electronic and energetic parameters associated with the studied molecules. The predictive ability of the built models, which is obtained by two methods (MLR and MNLR), showed that the built models are statistically significant. The QSAR modeling results revealed that the six molecular descriptors of lowest unoccupied molecular orbital energy (ELUMO), electrophilicity index (ω), molar refractivity (MR), aqueous solubility (Log S), topological polar surface area (PSA), and refractive index (n) significantly correlated to the biological inhibitory activity of piperazine derivatives. Using QSAR models and in silico pharmacokinetic profiles predictions, five new candidate compounds are selected as potential inhibitors against cancer.

Chance-constrained stochastic optimal control of epidemic models: A fourth moment method-based reformulation

This work proposes a methodology for the reformulation of chance-constrained stochastic optimal control problems that ensures reliable uncertainty management of epidemic outbreaks. Specifically, the chance constraints are reformulated in terms of the first four moments of the stochastic state variables through the so-called fourth moment method for reliability. Moreover, a spectral technique is employed to obtain surrogate models of the stochastic state variables, which enables the efficient computation of the required statistics. The practical implementation of the proposed approach is demonstrated via the optimal control of two different stochastic mathematical models of the COVID-19 transmission. The numerical experiments confirm that, unlike those reformulations based on the Chebyshev–Cantelli’s inequality, the proposed method does not exhibit the undesired outcomes that are typically observed when a higher precision is required for the risk level associated to the given chance constraints.

Analysis of the thermomechanical behavior of a three-layer rectangular plate of the ceramic-metal-ceramic structure due to non-stationary convective heating

A rectangular isotropic layered plate is considered, which is convectively heated by the external environment. The thermal stress state of the plate is determined in two stages. At the first stage, the nonstationary temperature field is determined from the ratios of the non-stationary thermal conductivity problem. At the second stage, using the five-modal mathematical model of the shear theory of thermoelasticity, the parameters of the stress-strain state are determined.

Enhanced energy harvesting in low-velocity water by downstream interference for piezoelectric energy harvester

The vibration of a single-degree-of-freedom bluff body positioned in water is intensified by the positive excitation, which is affected by the upstream interfering body and also by the downstream obstacles. This paper investigates the effect of downstream interference on galloping piezoelectric energy harvester performance. A mathematical model of the piezoelectric energy harvester under disturbance is established based on the extended Hamilton’s principle, and the theoretical output is further derived. The accuracy of proposed model is verified by the results of circulating water channel experiment. The effect of interference shape and approximate spacing (L/D) on system output is further analyzed, and the results show that the harvester performance is substantially improved when the distance between the bluff body and downstream interference is sufficiently small, and the interference is an elliptical cylinder with an aspect ratio of 0.6, i.e., the output power is 0.624 mW, which is improved by 24.39 % when L/D=1.8 and U=0.5m/s. Precise numerical calculations are further utilized to indicate that the harvester’s output performance is optimal when the downstream interference angle is 30°.

Development and evaluation of a mathematical model of dry granulation of molten blast-furnace slag

Development and evaluation of a mathematical model of dry granulation of molten blast-furnace slag

On plutonium-241 and americium in the two-component nuclear energy system

The paper deals with the influence of the strategy for using separated plutonium from spent fuel of thermal and fast reactors, as well as homogeneous burning of americium in the BN reactor core on the balance of americium in the Russian nuclear fuel cycle throughout the 21st century. The assessment is carried out with the use of mathematical modeling of nuclear materials movement including nuclide transformations throughout the nuclear energy system based on the CYCLE code. Scenario modeling of the americium and Pu-241 accumulation was carried out in Russia’s two-component nuclear energy system model with thermal (VVER) and fast (BN) reactors. In so doing, spent nuclear fuel (SNF) reprocessing was simulated in 2 options: as priority reprocessing of SNF of VVER reactors (1) or SNF of BN reactors (2). In addition to americium accumulation in the system without burning, the accumulation of this actinide was studied taking into account its homogeneous burning in the MOX-fuel of fast reactors at the level of its equilibrium content of ~1%. It has been shown that the priority reprocessing of VVER spent fuel makes it possible to reduce the americium accumulation by the end of the century by ~8 tons, and the effect is achieved by using freshly separated plutonium with short-term cooling, thus, by priority the americium source is eliminated, without directly handling it. Homogeneous addition of americium to the fuel of fast reactors of the BN-1200 type at a level of ~1% makes it possible to stop accumulation of americium in a two-component energy system by 2070, stabilizing it at a level of ~40 tons in the scenario with priority reprocessing of VVER SNF and ~50 tons in the scenario with priority reprocessing of BN SNF.

Research on Wellbore Integrity Evaluation Model of CO2 Enhanced Composite Fracturing

CO2 injection composite fracturing is an effective method for shale oil and gas well development. The downhole casing is prone to uniform corrosion, pitting, perforation, and even corrosion fracture in the CO2 environment. Therefore, it is particularly important to reveal the physical characteristics of CO2 under actual geological conditions and the impact of CO2 corrosion on the performance of casing. A mathematical model for the temperature and pressure field of CO2 in the wellbore under fracturing conditions is established in this paper, and the temperature and pressure distribution along the depth of the well is calculated. By optimizing the CO2 state equation and using the S-W equation, Lee model, and RK model to calculate the CO2 density, viscosity and compression factor, respectively, the phase distribution pattern of CO2 along the actual wellbore is obtained. Through CO2 corrosion tests on the casing, the influence of temperature and CO2 concentration on the corrosion rate of the casing is clarified. The peak corrosion rate of Q125 steel corresponds to 80 °C, and the corrosion rate increases with the increase in CO2 concentration. Finally, a prediction model for the uniform corrosion rate of casing under different temperatures and CO2 concentration conditions is obtained, which can provide technical support for the design of CO2-enhanced fracturing technology.

Generalized mathematical model applied to a silica sand laboratory-controlled mill: Derivation of simplified ceramic ball entrance flux, ball wear consumption, and mass distribution functions

A laboratory-controlled milling process of silica sand was carried out using aluminum oxide balls of three different sizes. The ball wear kinetic equations were experimentally obtained from the evolution curves of the ball diameter as a function of the operating time. From a generalized model, the ball entrance flux and ball wear consumption were calculated using exact two-parameter solution functions. One-parameter ball entrance flux and ball wear consumption functions were proposed to perform calculations that accurately describe the values provided by the two-parameter functions. In addition, a compact form of the ball mass distribution function is found. This set of simplified equations can be suitable for fast calculations in the milling industry.

A mathematical model describing the tip-stalk regulation in angiogenesis

Angiogenesis is the process of new blood vessel growth from existing vessels, involving extensive cell signaling. Under normal conditions, new vessels are robust and organized, with a balance among angiogenesis factors. In abnormal conditions, such as tumor development, vessels are stunted and tangled due to an imbalance of these factors. Pathological angiogenesis stimulates rapid vessel growth to feed the oxygen and nutriente starved tumor. Inhibiting angiogenesis can cause side effects like hypertension, thrombosis, and fatigue. To better understand this process, significant effort has gone into studying signaling pathways, contributing to drug development for diseases like cancer. This study presents a mathematical model describing angiogenesis on a microscopic scale, comparing its results with experimental data on vascular network topology. The model, implemented in MatLab®, uses ordinary differential equations to represent cell behavior. Results show that altering VEGF (Vascular Endothelial Growth Factor) disrupts system balance, impacting angiogenesis and possibly explaining differences in network topology seen experimentally.

A mathematical model for a buried source in the layered reduced micropolar half-space

A mathematical model for a buried source in the layered reduced micropolar half-space

The influence of unconventional assembly techniques on the comfort indicators of waterproof materials

The present paper aims to highlight the correlations between the comfort indicators of waterproof cotton-based fabrics, and the specific parameters of unconventional assembly technology. The materials considered include layers of Gore-Tex film, serving as substitutes for waterproof materials, intended to manufacture outerwear products such as protective equipment (jackets and overalls), which are breathable waterproof membranes. The comfort indicator values were obtained through standardised methods, and data processing and representation in two-dimensional (2D) and three-dimensional (3D) systems using correlation/graphing methods were carried out in Excel software, and using Jandel Table Curve 3D v2. Although experimental research can be extended to include specific functions related to durability indicators, this study focused theoretically and experimentally on how the variation in temperature of the low-pressure hot air jet can lead to changes in the vaporization coefficient, air permeability index, and thermal conductivity coefficient. The relationship between the comfort indicator values (thermal conductivity coefficient, air permeability index, and vapour permeability coefficient) of the considered materials and the treatment parameters of the installation (pressure, temperature, velocity) is expressed through statistically adequate mathematical models, highlighted by a correlation coefficient R = 0.983, with significance certified by the Fischer test. The study of comfort indicators was conducted under optimized treatment parameters, ensuring durability and presentation value functions in the treatment zone remain unchanged compared to those of the base materials.

A Multiscale Mathematical Model for the Fetal Blood Circulation of the Second Half of Pregnancy.

Doppler ultrasound is a commonly used method to assess hemodynamics of the fetal cardiovascular system and to monitor the well-being of the fetus. Indices based on the velocity profile are often used for diagnosis. However, precisely linking these indices to specific underlying physiology factors is challenging. Several influences, including wave reflections, fetal growth, vessel stiffness, and resistance distal to the vessel, contribute to these indices. Understanding these data is essential for making informed clinical decisions. Mathematical models can be used to investigate the relation between velocity profiles and physiological properties. This study presents a mathematical model designed to simulate velocity wave propagation throughout the fetal cardiovascular system, facilitating the assessment of factors influencing velocity-based indices. The model combines a one-fiber model of the heart with a 1D wave propagation model describing the larger vessels of the circulatory system and a lumped parameter model for the microcirculation. Fetal growth from 20 to 40 weeks of gestational age is incorporated by adjusting cardiac and circulatory parameter settings according to scaling laws. The model's results, including cardiac function, cardiac output distribution, and volume distribution, show a good agreement with literature studies for a growing healthy fetus from 20 to 40 weeks. In addition, Doppler indices are simulated in various vessels and agree with literature as well. In conclusion, this study introduces a novel closed-loop 0D-1D mathematical model that has been verified against literature studies. This model offers a valuable platform for analyzing factors influencing velocity-based indices in the fetal cardiovascular system.

Optimization of Fuzzy Mathematical Model of Regular Octagon-Shaped Parking Space

In the vigorous development of the city population, there is a need to set up clear dimensions for the parking space. Car parking plays a significant part in the residential apartments and commercial buildings. Roadside parking spaces will create a huge traffic problem if the parking lots are not properly designed. Sometimes, it leads to the accident. Hence, keeping all these causes in mind, the flexible parking space is the necessary of the time. In the proposed research work, the parking space considered in the problem is of a regular octagon shape, and the mathematical model is developed under a fuzzy environment. LINGO Optimization Software is used to solve the mathematical model and MATLAB(Matrix Laboratory) is used to define the fuzzy variable. At the outset, the results will reveal the importance of making the length of the parking lot under fuzzy environment.

Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine

Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.

Mathematical Modelling of Tensile Mechanical Behavior of a Bio-Composite Based on Polybutylene-Succinate and Brewer Spent Grains

A model based on the fitting of stress–strain data by tensile tests of bio-composites made of a bioplastic (polybutylene succinate (PBS)) and brewer spent grain filler (BSGF) is developed. Experimental tests were performed for various concentrations of BSGF in the range from 2% to 30%. The model is suitable for describing the elastic–plastic behavior of these materials in terms of two mechanical parameters, tensile stress and tensile stiffness (or Young’s modulus), depending on the filler concentration. The mechanical characteristics, derived from the fit parameters, show good agreement with the experimental data. The mathematical model used here could be an important aid for the experimentation and manufacturing process as it allows the prediction of the mechanical tensile parameters of a mixture with different filler concentrations, avoiding the long and complex preparation cycle of bio-composites, as well as the specific mechanical tests. The physical properties required by the objects created with the PBS–BSGF bio-composite by the partners/stakeholders of the research project co-financing this research can be quite different; therefore, a mathematical model that predicts some of the mechanical properties in terms of the mixture composition may be useful to speed up the selection of the required amount of BSGF in the mixture.

In silico assessment of CAR macrophages activity against SARS-CoV-2 infection

Macrophage engineering with chimeric antigen receptor is a promising technique first applied to the treatment of tumours and recently suggested as a possible immunotherapeutic route against the COVID-19 disease. Four immunotherapies based on engineered macrophages have been tested in vitro revealing promising, with one of them acting without increasing the cytokines level. We present a mathematical model aimed at the evaluation of both the SARS-CoV-2 virions dynamics and the cytokines production induced, while such newly developed constructs interact with the immune system once administered. The importance of the study lies both in monitoring the dynamics of the infection and in evaluating the cytokine production, since clinical studies show that in critical COVID-19 patients an abnormal cytokines production occurs, a concern to be accounted for in designing appropriate therapeutic strategies. The mathematical model was built in the context of the continuum approach of the mass conservation, while the numerical simulations have been performed introducing parameters deduced from the experiments, using the finite element method. The model simulations allow to analyse and to compare the immune mechanisms underlying the virus dynamics, deepening the investigation for two selected immunotherapies, suggesting that a synergistic work of involved cytokines with phagocytic activity of macrophages occurs. The best SARS-CoV-2 clearance relies not only on the phagocytic capacity of the engineered macrophages, but also on the production of T-lymphocytes, pro- and anti-inflammatory cytokines which in the two cases examined in depth can decrease by 99.7 %, 99.6 % and 69 % respectively, passing from the most effective immunotherapy to the least effective one. This study is the first mathematical model that analyses the dynamics of macrophages engineered to fight the COVID-19, and paves the way for their possible exploitation against such a challenging disease, going beyond existing models involving other immune cells.

How Scheduled Maintenance Affects Anaerobic Digester Supervision Through Modelling: A Practical Approach

Anaerobic digestion plays a crucial role in the transition toward a circular economy. Incorporating system supervision through mathematical modelling can enhance control and resilience. This study aims to assess the impact of scheduled digester maintenance on the effectiveness of modelling as a tool for monitoring and control. Data from a pilot-scale plug-flow digester were analyzed using an adapted ADM1 model. The maintenance involved halting the digester and removing sedimented solids. Model calibration indicated solid retention in the first two zones of the reactor, while the hydrolysis coefficient and biogas potential remained at 0.122 d−1 and 100.4 mL CH4/gVS, respectively. The average biogas production decreased from 156 to 109 mL/gVS pre- and post-maintenance. Simulations showed a decline in the model’s predictive accuracy after maintenance. To improve model fit, the initial conditions, solids retention, and kinetic parameters were adjusted. Optimal performance was achieved with khyd at 0.045 d−1 and B0 at 52.28 mL gVS−1, revealing an issue with the digester’s heating system. In conclusion, maintenance can significantly alter digester conditions, requiring model recalibration to maintain its effectiveness as a digital copilot for process supervision.

Identification of roughness coefficients based on recycled steel pipes using various mathematical models

Identification of roughness coefficients based on recycled steel pipes using various mathematical models

Mathematical Modeling and Indirect Carbon Emission Reduction Analysis of Urban Wastewater Treatment Systems Under Different Temperature Conditions

In the context of achieving the two-carbon target, this study utilized a wastewater treatment plant in Shenyang City as a case study to accurately calculate indirect emissions related to energy and chemical consumption within the energy-intensive wastewater treatment industry. Sumo software was employed for precise mathematical modeling. Considering the operational characteristics of wastewater treatment plants in cold regions, this study innovatively divided the annual operation cycle into two periods, namely normal temperature and low temperature, and determined the optimal operational parameters under a low-carbon mode. The results indicate that precise regulation of dissolved oxygen concentration to 0.5–1.5 mg/L (normal temperature period) and 1–2 mg/L (low temperature period) can significantly reduce carbon emissions related to electricity consumption by 13,781.9 t CO2-eq. From the perspective of chemical consumption, adjusting the dosage of polyaluminum chloride (PAC) to 75% and sodium acetate to 70% during the normal temperature period can lead to a reduction in indirect carbon emissions of 1614.4 t CO2-eq compared to the same period last year. During the low-temperature period, by reducing the dosage of polyaluminum chloride to 80% and sodium acetate to 75%, the indirect carbon emissions can be reduced by 1557.3 t CO2-eq compared to the corresponding period last year. After optimization, USD 1.49 million can be saved. This study simulated the operation conditions of cold-region urban wastewater treatment plants at different times to effectively control carbon emissions resulting from energy and chemical consumption in wastewater treatment. This result can provide innovative ideas for energy saving and carbon reduction in cold-region wastewater treatment plants.

Nonlinear vibrations and static bifurcation of a hyperelastic pipe conveying fluid

This study investigates the free and forced nonlinear vibrations, along with the static bifurcation behavior, of a fluid transmission hyperelastic pipe supported by clamped ends. Both geometrical and material nonlinearities are taken into account. The mathematical model is grounded in Euler–Bernoulli beam theory, incorporating von Kármán nonlinearity to capture the complexities of the system. For the hyperelastic materials, the strain energy function proposed by Yeoh is employed. Considering that the lowest critical velocity of the fluid flow is associated with the first mode, after deriving the governing equation using Hamilton’s principle, Galerkin discretization is applied to obtain the reduced order model in the first mode. Analysis of static bifurcation and stability is performed and critical velocity values of fluid flow are determined. The analysis of free and forced vibrations of the hyperelastic pipe is conducted using the method of multiple time scales, specifically focusing on the sub-critical velocity range of fluid flow, which corresponds to the unbuckled state of the pipe. This approach allows for a comprehensive examination of how fluid flow velocity influences the frequency characteristics of free vibrations, as well as the frequency response in the vicinity of the main resonance. The results obtained from this study can significantly enhance our understanding of the design and application of hyperelastic pipes in various fluid transfer scenarios. By elucidating the dynamic behavior and critical parameters associated with these pipes, the findings can inform engineering practices and contribute to the optimization of systems that utilize hyperelastic materials for fluid conveyance.