Mathematical Model Research Articles

Length control emerges from cytoskeletal network geometry

Many cytoskeletal networks consist of individual filaments that are organized into elaborate higher-order structures. While it is appreciated that the size and architecture of these networks are critical for their biological functions, much of the work investigating control over their assembly has focused on mechanisms that regulate the turnover of individual filaments through size-dependent feedback. Here, we propose a very different, feedback-independent mechanism to explain how yeast cells control the length of their actin cables. Our findings, supported by quantitative cell imaging and mathematical modeling, indicate that actin cable length control is an emergent property that arises from the cross-linked and bundled organization of the filaments within the cable. Using this model, we further dissect the mechanisms that allow cables to grow longer in larger cells and propose that cell length-dependent tuning of formin activity allows cells to scale cable length with cell length. This mechanism is a significant departure from prior models of cytoskeletal filament length control and presents a different paradigm to consider how cells control the size, shape, and dynamics of higher-order cytoskeletal structures.

Deep learning for autosegmentation for radiotherapy treatment planning: State-of-the-art and novel perspectives.

The rapid development of artificial intelligence (AI) has gained importance, with many tools already entering our daily lives. The medical field of radiation oncology is also subject to this development, with AI entering all steps of the patient journey. In this review article, we summarize contemporary AI techniques and explore the clinical applications of AI-based automated segmentation models in radiotherapy planning, focusing on delineation of organs at risk (OARs), the gross tumor volume (GTV), and the clinical target volume (CTV). Emphasizing the need for precise and individualized plans, we review various commercial and freeware segmentation tools and also state-of-the-art approaches. Through our own findings and based on the literature, we demonstrate improved efficiency and consistency as well as time savings in different clinical scenarios. Despite challenges in clinical implementation such as domain shifts, the potential benefits for personalized treatment planning are substantial. The integration of mathematical tumor growth models and AI-based tumor detection further enhances the possibilities for refining target volumes. As advancements continue, the prospect of one-stop-shop segmentation and radiotherapy planning represents an exciting frontier in radiotherapy, potentially enabling fast treatment with enhanced precision and individualization.

Modelling on COVID-19 control with double and booster-dose vaccination

COVID-19 vaccines have been illustrated to lessen the growth of sickness caused by the virus effectively. In any case, inoculation has consistently been controversial, with differing opinions and viewpoints. This has compelled some individuals to decide against receiving the vaccine. These divergent viewpoints have had a trivial impact on the epidemic’s dynamics and the disease’s development. In response to vaccinated individuals still falling ill, many countries have implemented booster vaccines to protect further.In this specific investigation, a mathematical model composed of seven compartments is employed to examine the effectiveness of a booster dose in preventing and treating the transmission of COVID-19. The principles of mathematics are employed to analyse and investigate the dynamics of the disease. Using a qualitative prototype analysis, we acquired valuable insights into its effectiveness. One essential aspect is the basic reproduction number, a critical determinant of the disease’s spread. This calculation is determined by studying the system’s equilibrium and evaluating its stability.Furthermore, we examined the balance from a local and global viewpoint, considering the possibility of bifurcation and the model’s reproductive number sensitivity index. Through numerical simulations, we have visually illustrated the analytical findings outlined in this research paper and presented a thorough examination of the efficacy of booster shots as a preventive and therapeutic measure in the spread dynamics of COVID-19.

Conflict Detection in Language Processing: Using Affect Control Theory to Predict Neural Correlates of Affective Incongruency in Social Interactions

AbstractAffect control theory (ACT) is a sociological theory of meaning processing in social interactions. Meaning, according to ACT, derives from cultural institutions and situational affordances, having denotative (declarative) as well as connotative (affective) properties. Mathematical formalizations of ACT allow predictions of affective incongruency (in the terminology of ACT, deflection), which arises from conflicting institutional and situational meanings in a given interaction context. Although ACT is theoretically consistent, its propositions regarding cognitive and affective processing have rarely been tested. The present study fills this gap by investigating the neural processing of affective incongruency in linguistic descriptions of social interactions. Following a neurosociological paradigm, the study draws on neurocognitive evidence on the effects of words’ affective content on word processing as well as on a previous electroencephalography study that investigated processing of affective incongruency using event-related brain potentials. We hypothesized that affective incongruency is associated with activation in the anterior cingulate cortex (ACC), a brain area known for conflict processing. To test this hypothesis, we replicated the electroencephalography study using functional magnetic resonance imaging: We visually presented sentences describing social interactions to 23 participants in a silent reading task while measuring differences in the hemodynamic response in two conditions of affective congruency. Results show expected increases in neural activity for affectively incongruent sentences in the left ACC, supporting the assumption that affective language content influences meaning-making at very early semantic processing stages. The results also add to the emerging neuroscientific evidence for ACT’s mathematical model of impression formation.

Development of a Simple Analytical Model to Facilitate Preoperative Surgical Planning in Valve-Sparing Aortic Root Replacement.

Valve-sparing root replacement (VSRR) is attractive for aortic root dilation as it preserves the native aortic valve (AoV). Low effective height (eH) after reconstruction is a risk factor for repair failure and reoperation. We developed and validated a quantitative AoV repair strategy to reliably restore normal valve proportions to promote long-term function. Normal AoV proportions were used to derive geometric relationships for sinotubular junction diameter (DSTJ), free edge length (FEL), free edge angle, and commissure height. These relationships informed two models for predicting eH following VSRR: (1) assuming valve symmetry and (2) accounting for valve asymmetry. Porcine heart (n = 6) ex vivo validation was performed under 4 VSRR scenarios: "Ideal" (tube graft size targeting FEL/DSTJ = 1.28), "Oversized" (one graft size larger than Ideal), "Undersized" (two sizes smaller), and "Undersized + Plicated" (FEL/DSTJ = 1.28 restored with leaflet plication). Our analytical models predicted eH using preoperative measurements and estimated reconstructed dimensions. The Oversized graft exhibited similar eH to Ideal but higher regurgitation in the ex vivo model, whereas the Undersized graft demonstrated lower eH and regurgitation. Plication in the Undersized graft restored valve function (regurgitation & eH) similar to Ideal in the ex vivo model and above Ideal in the analytical models. Both analytical models predicted ex vivo eH well except in the Oversized and Undersized + Plicated conditions. Utilizing measurements from preoperative imaging and simple mathematical models, patient-specific operative plans for VSRR can be created by estimating valve dimensions necessary to achieve favorable valve features post-repair. Clinical application of this approach promises to improve consistency in achieving optimal long-term dimensions and durability.

Modeling uncertainty: the impact of noise in T cell differentiation

BackgroundThe regulatory mechanisms guiding CD4 T cell differentiation are complex and are further influenced by intrinsic cell variability along with that of microenvironmental cues, such as cytokine and nutrient availability.ObjectiveThis study aims to expand our understanding of CD4 T cell differentiation by examining the influence of intrinsic noise on cell fate.MethodologyA model based on a complex regulatory network of early signaling events involved in CD4 T cell activation and differentiation was described in terms of a set of stochastic differential equation to assess the effect of noise intensity on differentiation efficiency to the Th1, Th2, Th17, Treg, and TFH effector phenotypes under defined cytokine and nutrient conditions.ResultsThe increase of noise intensity decreases differentiation efficiencies. In a microenvironment of Th1-inducing cytokines and optimal nutrient conditions, noise levels of 3%, 5% and 10% render Th1 differentiation efficiencies of 0.87, 0.76 and 0.62, respectively, underscoring the sensitivity of the network to random variations. Further increments of noise reveal that the network is relatively stable until noise levels of 20%, where the resulting cell phenotypes becomes heterogeneous. Notably, Treg differentiation showed the highest robustness to noise perturbations. A combined Th1-Th2 cytokine environment with optimal nutrient levels induces a dominant Th1 phenotype; however, removal of glutamine shifts the balance towards the Th2 phenotype at all noise levels, with an efficiency similar to that obtained under Th2-only cytokine conditions. Similarly, combinations of Th1/Treg and Treg/Th17-inducing cytokines along with the removal of either tryptophan or oxygen shift the dominant Th1 and Treg phenotypes towards Treg and Th17 respectively. Model results are consistent with differentiation efficiency patterns obtained under well-controlled experimental settings reported in the literature.ConclusionThe stochastic CD4 T cell mathematical model presented here demonstrates a noise-dependent modulation of T cell differentiation induced by cytokines and nutrient availability. Modeling results can be explained by the network topology, which assures that the system will arrive at stable states of cell functionality despite variable levels of biological intrinsic noise. Moreover, the model provides insights into the robustness of the T cell differentiation process.

Volatilization of benzene on soil surface under different factors: evaluation and modeling

The volatilization of volatile organic compounds following a leakage event is a crucial mechanism that influences their migration and transformation in the soil. It is noteworthy that this process is intricately shaped by soil properties and environmental factors, exhibiting highly complex nonlinear relationships. However, there is currently no reliable mathematical model to predict the nonlinear relationship. To address this gap, the study conducted dynamic experiments considering various factors, including particle size, organic matter content, temperature, wind speed and moisture content. The volatilization rate (k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}), an important parameter in volatilization kinetics reflecting the speed of volatilization, was calculated by first-order kinetic principle. Finally, an innovative approach was introduced using a Back Propagation Neural Network (BPNN) model for prediction. The findings indicate that wind speed exerts the most significant impact on the volatilization rate of benzene among the examined factors. The application of BPNN demonstrates the model's accuracy in simulating benzene volatilization rates under diverse conditions. The results of K-fold cross-validation alleviate concerns of potential over-prediction, affirming the reliability of the constructed model. This research introduces a novel methodology for predicting volatilization parameters in real-world scenarios.

Nonlinear Interpretation of Resilient Modulus Parameters Considering Incremental Static and Dynamic Loading

The resilient modulus ( Mr) is typically interpreted as the average of the last five secant slopes of the cyclic stress-axial resilient strain curve from repeated loading triaxial tests. It is not uncommon to then fit mathematical models to the secant Mr to derive model parameters ( Ki, more commonly known as K1, K2, and K3) that are then used in pavement analysis. Some engineers also backcalculate Ki from a falling weight deflectometer test. Many researchers use an incremental loading procedure to analyze pavements. When doing so, it is important to consider the nonlinear load-deformation behavior, which is considered only coarsely in the secant slope approach. Some incremental loading procedures assume the geomaterial to be nonlinear elastic while a dynamic finite element analysis typically assumes the geomaterials to be nonlinear and viscoelastic, that is, having springs and dashpots. With the latter, additional damping parameters to represent the viscoelastic effects are required. This paper compares Ki parameters estimated using linear regression on a log transformation of the Mechanistic–Empirical Pavement Design Guide (MEPDG) Mr model, which is a non-viscoelastic secant Mr approach, with those obtained using nonlinear regression of the time dependent deformations when interpreting the Mr test using incremental loading of a: 1) nonlinear elastic geomaterial; and 2) nonlinear viscoelastic geomaterial with inertial mass. The results show that the estimated Ki parameters governing the geomaterial nonlinearity are substantially affected by the estimation method and that the second alternative approach can model hysteresis well.

Machine Learning-Driven Biomarker Discovery for Skeletal Complications in Type 1 Gaucher Disease Patients

Type 1 Gaucher disease (GD1) is a rare, autosomal recessive disorder caused by glucocerebrosidase deficiency. Skeletal manifestations represent one of the most debilitating and potentially irreversible complications of GD1. Although imaging studies are the gold standard, early diagnostic/prognostic tools, such as molecular biomarkers, are needed for the rapid management of skeletal complications. This study aimed to identify potential protein biomarkers capable of predicting the early diagnosis of bone skeletal complications in GD1 patients using artificial intelligence. An in silico study was performed using the novel Therapeutic Performance Mapping System methodology to construct mathematical models of GD1-associated complications at the protein level. Pathophysiological characterization was performed before modeling, and a data science strategy was applied to the predicted protein activity for each protein in the models to identify classifiers. Statistical criteria were used to prioritize the most promising candidates, and 18 candidates were identified. Among them, PDGFB, IL1R2, PTH and CCL3 (MIP-1α) were highlighted due to their ease of measurement in blood. This study proposes a validated novel tool to discover new protein biomarkers to support clinician decision-making in an area where medical needs have not yet been met. However, confirming the results using in vitro and/or in vivo studies is necessary.

Applications of neural networking in Eyring-Powell nanofluid dynamics on a rotating surface in a porous medium

One of the fundamental aspects of solving difficult and nonlinear mathematical ideas is the use of Artificial Neural Networks due to their exceptional efficiency in handling such problems. In many complex fields such as computational fluid system, biological computation, and biotechnology, a distinct computing structure is provided by Artificial Neural Networks, which is extremely valuable. The main purpose of this article is to dig out the abilities of the Levenberg-Marquardt technique using back-propagation artificial neural networks regarding the fluid mechanics and the heat transport assessment in nanoparticles. This interdisciplinary field explores heat and mass transfer through objects and fluids, and their impacts on temperature as well as concentration distributions. With the help of mathematical modelling and numerical solution methodologies, researchers can simulate and analyze these processes. The present analysis communicates the Eyring-Powell fluid flow caused by a rotating disk placed in the horizontal direction. The fluid flow over a rotating disk through non-linear partial differential equations is modeled. After converting the partial differential equations to ordinary ones, they are tackled numerically through shooting technique. The Levenberg-Marquardt algorithm using back-propagation artificial neural networks technique is used with reference datasets, having 70 % training, 15 % testing, and 15 % to validation. The method is validated with the help of mean squared error, error histogram and comprehensive regression analysis. These figures show the accuracy of the proposed method for solving nonlinear problems. Flow features such as velocity, temperature as well as the concentration profiles are exemplified quantitatively and have been graphically discussed. Velocity of the fluid decreases for porosity and increases for fluid parameter while temperature increases for thermophoresis and Brownian motion parameters. Consistency is shown by getting a minimum absolute error approaching zero, showing the strength of the proposed approach.

A non-memory-based functional neural framework for animal caching behavior

The brain’s extraordinary abilities are often attributed to its capacity to learn and adapt. But memory has its limitations, especially when faced with tasks such as retrieving thousands of food items—a common behavior in scatter-hoarding animals. Here, we propose a brain mechanism that may facilitate caching and retrieval behaviors, with a focus on hippocampal spatial cells. Rather than memorizing the locations of their caches, as previously hypothesized, we suggest that cache-hoarding animals employ a static mechanism akin to hash functions commonly used in computing. Our mathematical model aligns with the activity of hippocampal spatial cells, which respond to an animal’s positional attention. We know that the region that activates each spatial cell remains consistent across subsequent visits to the same area but not between areas. This remapping, combined with the uniqueness of cognitive maps, produces persistent hash functions that can serve both food caching and retrieval. We present a simple neural network architecture that can generate such a probabilistic hash that is unique to the animal and not sensitive to environmental changes. This mechanism could serve a virtually boundless capacity for the encoding of any structured data.

Numerical Calculation and Application for Crushing Rate and Fracture Conductivity of Combined Proppants

Proppant is one of the key materials for hydraulic fracturing. For special situations, such as middle-deep reservoirs and closure pressures ranging from 40 MPa to 60 MPa, using a single proppant cannot solve the contradiction between performance, which means crushing rate and fracture conductivity, and cost. However, using combined proppants is an economically effective method for hydraulic fracturing of such special reservoirs. Firstly, for different types, particle sizes, and proportions of combined proppants, various contact relationships between proppant particles are considered. The random phenomenon of proppant particle arrangement is described using the Monte Carlo method, and the deterministic phenomenon of proppant particles is processed using an optimization model, achieving computer simulation of the microscopic arrangement of proppant particles. Secondly, a mathematical model for the force analysis of combined proppant particles is established, and an improved singular value decomposition method is used for numerical solution. A computational model for the crushing rate and fracture conductivity of combined proppants is proposed. Thirdly, the numerical calculation results are compared and discussed with the test values, verifying the accuracy of the computational model. Finally, the application of combined proppants is discussed, and a model for optimizing the proportion of combined proppants is proposed. The onsite construction technology is introduced, and the cost and economic benefits of combined proppants are compared with those of all ceramic particles and excessive all-quartz sand. It is proved that combined proppants can balance performance and price, and are an economically effective method for hydraulic fracturing of special reservoirs. The research results can select the optimal proppant material and optimize the combination of different proppant types, which can help achieve cost reduction and efficiency increase in oil and gas development.

Hydrodynamic Evaluation of a Filtering Hydrocyclone for Solid Particle/Water Separation

A conventional hydrocyclones is a versatile equipment with a high processing capacity and low maintenance cost. Currently, several studies aim to alter the typical structure of the conventional hydrocyclone in order to modify its performance and purpose. For this, filtering hydrocyclones have emerged, where a porous membrane replaces the conic or cylindrical wall. During the operation of this equipment, in addition to the traditionally observed streams (feed, underflow, and overflow), there is a liquid stream resulting from the filtration process, commonly referred to as filtrate. This work proposes to numerically investigate the solid particle/liquid water separation process in a filtering hydrocyclone using the commercial software Ansys CFX® 15.0. The proposed mathematical model for the study considers three-dimensional, steady state and turbulent flow, using the Eulerian–Eulerian approach and the Shear Stress Transport (SST) turbulence model. This study presents and analyzes the volume fraction, velocity, and pressure fields, along with flowlines and velocity profiles. The results indicate that the proposed model effectively captures the fluid dynamic behavior within the filtering hydrocyclone, highlighting higher pressures near the porous membrane and a higher concentration of solid particles in the conical region, with water being more concentrated in the cylindrical part of the hydrocyclone. Additionally, the findings show that the volumetric flow rate of the filtrate significantly influences the internal flow dynamics, with conventional hydrocyclones demonstrating higher pressure gradients compared to the proposed filtering hydrocyclone.

Modeling of servo dynamic stiffness for multiple-periodic repetitive learning control system

Servo dynamic stiffness is a pivotal index in characterizing the rejecting performance for the exogenous periodic disturbances of the repetitive learning control system. In this paper, the mathematical modeling of the servo dynamic stiffness for the well-designed repetitive learning control system with multiple-periodic signals is studied by the frequency analysis method. To analysis the complex form of the servo dynamic stiffness, the magnitudes of the direct (real part) and quadrature (imaginary part) servo dynamic stiffness at harmonics of the disturbance are discussed based on the parameters of the repetitive learning controller. An illustrated example of the two linear servomotors with the mechanical coupling is given in this study. Computer simulation are presented to illustrate the effect of the proposed measurement method of the servo dynamic stiffness for the multiple-periodic repetitive learning control system. The proposed servo dynamic stiffness modeling can be used to accurate design the parameters of the repetitive learning control system, such that the batter control performance of the repetitive learning control system at most of the harmonics of the multi-periodic input signal can be achieved.

A New Modeling Approach and Comprehensive Monitoring of Electrical Faults Through Spectral Analysis in DSIM

The objective of this study is to evaluate the dependability of double-star induction machines by employing meticulous monitoring and intelligent handling of potential electrical malfunctions that may arise during their functioning. Specifically, the research delves into the examination of three distinct fault types: rotor bar breakage, stator phase opening, and inter-turn short circuit. Utilizing a mathematical model developed in the natural reference frame (abc), our aim is to comprehensively delineate both normal and faulty operational scenarios. To categorize and gauge the gravity of identified faults, we employ a methodology rooted in spectral analysis. In order to ensure continuous machine operation, especially in instances of stator phase opening, our proposed mitigation approach entails intentionally opening a secondary phase positioned at a 90-degree angle to the faulty phase. This strategic alteration transforms the machine into a dual two-phase configuration. Through rigorous simulation analyses, our findings underscore the efficacy and pragmatic viability of the devised fault detection technique, offering valuable insights into the domain of electrical machine reliability and fault management.

Exploring tumor-induced immunosuppression dynamics by myeloid-derived suppressor cells: insights via a fractional-order mathematical model

Exploring tumor-induced immunosuppression dynamics by myeloid-derived suppressor cells: insights via a fractional-order mathematical model

Optimization and Kinetic Study of Manganese Leaching from Pyrolusite Ore in Hydrochloric Acid Solutions with Oxalic Acid

AbstractThe leaching behavior of pyrolusite minerals was examined in hydrochloric acid solutions, including oxalic acid, to evaluate the influence of various experimental conditions. The optimum parameters for the leaching process were found in the first stage, and the process's kinetics were assessed in the second. The concentrations of oxalic acid, hydrochloric acid, and temperature were chosen as independent variables in the optimization experiments, with the central composite design used to analyze the experimental data. The optimum concentrations for oxalic acid, hydrochloric acid, and temperature were determined to be 0.75 mol/L, 1.2 mol/L, and 60 °C, respectively. The leaching rate was determined to be 97.4% for 120 min of response time in optimum situations. The kinetic assessment experiments studied the effects of solid/liquid ratio, particle size, stirring speed, and temperature on the manganese leaching rate from pyrolusite. In the studies, the leaching rate was shown to rise with increasing temperature and stirring speed, as well as with decreasing particle size and solid/liquid ratio. The kinetic analysis revealed that the leaching kinetics matched the mixed kinetic model, and a mathematical model for the leaching process was developed. This process's activation energy was determined to be 29.05 kJ/mol. Graphical Abstract

Study on the Fire Characteristics of Dual Fire Sources and the Difference in Power Temperature of Different Fire Sources in Tunnel

To investigate the combustion characteristics of multiple fire sources in the tunnel caused by ‘jumping’ discontinuous fire spread, we utilized scaled model experiments, numerical simulation software, and theoretical research. Our study focused on analyzing the influence of different fire source powers on the temperature characteristics of double fire sources in the tunnel. We examined the temperature characteristics, critical wind speed, and change rule under various wind speeds, fire source spacing, and fire source powers. Additionally, we explored the temperature characteristics, critical wind speed, and change rule of different fire source powers under varying wind speed conditions. The mathematical model for roof temperature decay and the temperature decay coefficients of dual source fires were established through the analysis of scale-down model experiments and numerical simulations. In comparison to single-source fires, the temperature variations in the tunnel of dual source fires exhibit a more intricate pattern, with higher average temperature and temperature peak values. These values are influenced by factors such as fire source spacing and power. Numerical simulation software was utilized to investigate the impact of fire source spacing at 10 m, 15 m, and 20 m, as well as the effect of varying fire source power on the temperature distribution within a tunnel under consistent fire source position and growth coefficient. The study revealed that, with consistent double fire source position and ventilation conditions in the tunnel, the upstream fire source exhibited greater power than the downstream fire source, resulting in the lowest average and peak temperatures in the tunnel. This observation could potentially enhance escape and rescue operations within the tunnel. Similarly, the lowest average and peak temperatures in the tunnel were also identified, offering potential benefits for optimizing escape and rescue strategies in tunnel scenarios.

Quantifying Plant Signaling Pathways by Integrating Luminescence-Based Biosensors and Mathematical Modeling

Plants have evolved intricate signaling pathways, which operate as networks governed by feedback to deal with stressors. Nevertheless, the sophisticated molecular mechanisms underlying these routes still need to be comprehended, and experimental validation poses significant challenges and expenses. Consequently, computational hypothesis evaluation gains prominence in understanding plant signaling dynamics. Biosensors are genetically modified to emit light when exposed to a particular hormone, such as abscisic acid (ABA), enabling quantification. We developed computational models to simulate the relationship between ABA concentrations and bioluminescent sensors utilizing the Hill equation and ordinary differential equations (ODEs), aiding better hypothesis development regarding plant signaling. Based on simulation results, the luminescence intensity was recorded for a concentration of 47.646 RLUs for 1.5 μmol, given the specified parameters and model assumptions. This method enhances our understanding of plant signaling pathways at the cellular level, offering significant benefits to the scientific community in a cost-effective manner. The alignment of these computational predictions with experimental results emphasizes the robustness of our approach, providing a cost-effective means to validate mathematical models empirically. The research intended to correlate the bioluminescence of biosensors with plant signaling and its mathematical models for quantified detection of specific plant hormone ABA.

Analysis of corneal biomechanical properties in different keratotopographic patterns of keratoconus

256 subjects (256 eyes) participated in the study: 174 healthy individuals (174 eyes) with normal corneas with different refraction and 82 patients (82 eyes) with keratoconus at stages 1, 2 and 3. Based on mathematical modeling, the biomechanical corneal properties with different patterns of keratoconus at stages 1, 2, and 3 were evaluated. Mathematical modeling made it possible to determine the dimensions and degrees of local corneal biomechanical properties reduction, which depended on the disease stage and practically did not change from the shape and keratopographic pattern localization.