INTRODUCTION: While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors. METHODS: We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions. RESULTS: Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions. DISCUSSION: Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to radiotherapy.

• Keywords
• Gompertz law, abscopal effect, immune response, immunotherapy, mathematical modeling, radiotherapy,
• MeSH
• Immunotherapy * methods   MeSH
• Combined Modality Therapy MeSH
• Humans MeSH
• Neoplasms * therapy   immunology   radiotherapy   MeSH
• Radiotherapy methods   MeSH
• Models, Theoretical MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH

This work focuses on mathematical modeling of removal of organic dyes from textile industry waste waters by a white-rot fungus Irpex lacteus in a trickle-bed bioreactor. We developed a mathematical model of biomass and decolorization process dynamics. The model comprises mass balances of glucose and the dye in a fungal biofilm and a liquid film. The biofilm is modeled using a spatially two-dimensional domain. The liquid film is considered as homogeneous in the direction normal to the biofilm surface. The biomass growth, decay and the erosion of the biofilm are taken into account. Using experimental data, we identified values of key model parameters: the dye degradation rate constant, biofilm corrugation factor and liquid velocity. Considering the dye degradation rate constant 1×10⁻⁵ kg m⁻³ s⁻¹, we found optimal values of the corrugation factor 0.853 and 0.59 and values of the liquid velocity 5.23×10⁻³ m s⁻¹ and 6.2×10⁻³ m s⁻¹ at initial dye concentrations 0.09433 kg m⁻³ and 0.05284 kg m⁻³, respectively. A good agreement between the simulated and experimental data using estimated values of the model parameters was achieved. The model can be used to simulate the performance of laboratory scale trickle-bed bioreactor operated in a batch regime or to estimate values of principal parameters of the bioreactor system.

• MeSH
• Color MeSH
• Coloring Agents MeSH
• Biodegradation, Environmental MeSH
• Biofilms MeSH
• Biomass MeSH
• Bioreactors * MeSH
• Time Factors MeSH
• Kinetics MeSH
• Waste Disposal, Fluid instrumentation   MeSH
• Computer Simulation MeSH
• Models, Theoretical * MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Names of Substances
• Coloring Agents MeSH

This work answers some questions related to detection of rheological properties of soft tissues exemplified in myometrium, stressed by external tensile force. In the first stage of the experiment the tissue samples were ciclically stressed and response loops were recorded. This test proved severe plastical deformation of samples, which is not usually being stated for living tissues. In addition to course, growth and stabilizing this deformation also energetical losses of individual hysteresis loops of the response were evaluated. In the second stage of the experiment the tissue samples were exposed to a loading force changed in step-wise manner in four steps. The sample response to each force step was processed and evaluated separately to obtain basic properties of used model. In next step, the changes in model characteristics were obtained and evaluated for each element in subsequent force steps. By reason of following easier interpretation, the quite simple visco-elastic model, defined by differential equation with analytic solution, is used. The results prove necessary to introduce in model both spring and damper constants dependent on the magnitude of the loading force and one damper with even time dependent constant. The interindividual variability of characteristic values of the model elements is surprisingly low. On the other side, they are strongly dependent on load magnitude. Complete mathematical model of uterine wall tissue is obtained by amending the principal equation by formulas describing changes in individual components of the model.

• MeSH
• Biomechanical Phenomena MeSH
• Adult MeSH
• Middle Aged MeSH
• Humans MeSH
• Stress, Mechanical MeSH
• Myometrium anatomy & histology   MeSH
• Elasticity MeSH
• Rheology * MeSH
• Aged MeSH
• Models, Theoretical * MeSH
• Check Tag
• Adult MeSH
• Middle Aged MeSH
• Humans MeSH
• Aged MeSH
• Female MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH

The influence of spatially modulated high gradient magnetic fields on cellular functions of human THP-1 leukemia cells is studied. We demonstrate that arrays of high-gradient micrometer-sized magnets induce i) cell swelling, ii) prolonged increased ROS production, and iii) inhibit cell proliferation, and iv) elicit apoptosis of THP-1 monocytic leukemia cells in the absence of chemical or biological agents. Mathematical modeling indicates that mechanical stress exerted on the cells by high magnetic gradient forces is responsible for triggering cell swelling and formation of reactive oxygen species followed by apoptosis. We discuss physical aspects of controlling cell functions by focused magnetic gradient forces, i.e. by a noninvasive and nondestructive physical approach.

• Keywords
• Apoptosis, Cell proliferation, Leukemia, Magnetic field, Modeling, Reactive oxygen species,
• MeSH
• Apoptosis MeSH
• Leukemia metabolism   pathology   MeSH
• Humans MeSH
• Magnetics * MeSH
• Stress, Mechanical MeSH
• Monocytes metabolism   pathology   MeSH
• Cell Line, Tumor MeSH
• Reactive Oxygen Species metabolism   MeSH
• Models, Theoretical * MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Names of Substances
• Reactive Oxygen Species MeSH

A mathematical model of myocardial perfusion based on the lattice Boltzmann method (LBM) is proposed and its applicability is investigated in both healthy and diseased cases. The myocardium is conceptualized as a porous material in which the transport and mass transfer of a contrast agent in blood flow is studied. The results of myocardial perfusion obtained using LBM in 1D and 2D are confronted with previously reported results in the literature and the results obtained using the mixed-hybrid finite element method. Since LBM is not suitable for simulating flow in heterogeneous porous media, a simplified and computationally efficient 1D-analog approach to 2D diseased case is proposed and its applicability discussed.

• Keywords
• advection–diffusion problem, contrast agent transport, lattice Boltzmann method, magnetic resonance imaging, mixed‐hybrid finite element method, myocardial perfusion,
• MeSH
• Finite Element Analysis * MeSH
• Contrast Media MeSH
• Coronary Circulation physiology   MeSH
• Humans MeSH
• Models, Cardiovascular * MeSH
• Computer Simulation MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH
• Names of Substances
• Contrast Media MeSH

Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The aim of this work is to examine that the Lung Cancer detection and treatment by introducing IL2 and anti-PD-L1 inhibitor for low immune individuals. Mathematical model is developed with the created hypothesis to increase immune system by antibody cell's and Fractal-Fractional operator (FFO) is used to turn the model into a fractional order model. A newly developed system TCDIL2Z is examined both qualitatively and quantitatively in order to determine its stable position. The boundedness, positivity and uniqueness of the developed system are examined to ensure reliable bounded findings, which are essential properties of epidemic models. The global derivative is demonstrated to verify the positivity with linear growth and Lipschitz conditions are employed to identify the rate of effects in each sub-compartment. The system is investigated for global stability using Lyapunov first derivative functions to assess the overall impact of IL2 and anti-PD-L1 inhibitor for low immune individuals. Fractal fractional operator is used to derive reliable solution using Mittag-Leffler kernel. In fractal-fractional operators, fractal represents the dimensions of the spread of the disease and fractional represents the fractional ordered derivative operator. We use combine operators to see real behavior of spread as well as control of lung cancer with different dimensions and continuous monitoring. Simulations are conducted to observe the symptomatic and asymptomatic effects of Lung Cancer disease to verify the relationship of IL2, anti-PD-L1 inhibitor and immune system. Also identify the real situation of the control for lung cancer disease after detection and treatment by introducing IL2 cytokine and anti-PD-L1 inhibitor which helps to generate anti-cancer cells of the patients. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.

• MeSH
• Cytokines MeSH
• Fractals MeSH
• Interleukin-2 * MeSH
• Humans MeSH
• Lung Neoplasms * drug therapy   MeSH
• Models, Theoretical MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH
• Names of Substances
• Cytokines MeSH
• Interleukin-2 * MeSH

BACKGROUND: Intraluminal irreversible electroporation (IRE) can be used for recanalizing occluded metal stents. However, optimal IRE parameters for consistent effects across different stent designs remain unclear. The aim of this study was to simulate the process of stent recanalization in silico by employing finite element analysis. METHODS: A virtual model of an occluded biliary stent with an experimental 3-electrode IRE catheter was developed. Electric field distribution, temperature changes, and potential ablation volumes were simulated across various parameters: IRE voltage (300 - 1300 V), stent wire width (0.1 - 0.5 mm) and stent mesh size (0.7 - 5.58 mm). Simulations incorporated five representative stent types commonly used in clinical practice. 685 unique simulations were conducted, analyzing 1162 unique values. RESULTS: Higher voltages generally led to larger ablation zones and increased temperatures. Thinner stent wires and larger mesh sizes also increased the extent of ablation zone. While in-stent ablation was largely independent of stent design, out-of-stent ablation was significantly impacted by mesh size and tissue thickness between the stent and irreversible electroporation electrodes. Voltages above 1000 V produced significant thermal effects, with substantial volumes of tissue heated above 50 °C. Specific stent designs exhibited variations in maximum temperature (72.1 - 83.1 °C) and ablation volume (8.7 - 14.7 mm3). CONCLUSION: Tailored IRE protocols for different stent designs are required due to differences in in- and out-stent ablation volumes. High voltages (>1000 V) induce both thermal and nonthermal ablation mechanisms.

• Keywords
• Irreversible electroporation, ablation, computer simulation, metal stents, temperature distribution,
• MeSH
• Electroporation * methods   MeSH
• Humans MeSH
• Stents * MeSH
• Models, Theoretical * MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH

Simul 5 Complex is a one-dimensional dynamic simulation software designed for electrophoresis, and it is based on a numerical solution of the governing equations, which include electromigration, diffusion and acid-base equilibria. A new mathematical model has been derived and implemented that extends the simulation capabilities of the program by complexation equilibria. The simulation can be set up with any number of constituents (analytes), which are complexed by one complex-forming agent (ligand). The complexation stoichiometry is 1:1, which is typical for systems containing cyclodextrins as the ligand. Both the analytes and the ligand can have multiple dissociation states. Simul 5 Complex with the complexation mode runs under Windows and can be freely downloaded from our web page http://natur.cuni.cz/gas. The article has two separate parts. Here, the mathematical model is derived and tested by simulating the published results obtained by several methods used for the determination of complexation equilibrium constants: affinity capillary electrophoresis, vacancy affinity capillary electrophoresis, Hummel-Dreyer method, vacancy peak method, frontal analysis, and frontal analysis continuous capillary electrophoresis. In the second part of the paper, the agreement of the simulated and the experimental data is shown and discussed.

• MeSH
• Cyclodextrins MeSH
• Electrophoresis, Capillary * MeSH
• Computer Simulation MeSH
• Stereoisomerism MeSH
• Models, Theoretical * MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Names of Substances
• Cyclodextrins MeSH

The previously developed mathematical model of CD4+ lymphocyte dynamics in HIV infection incorporated a homeostatic mechanism regulating production of both CD4+ and CD8+ lymphocytes. The model simulated the CD4+ lymphocyte dynamics well, but simulation of CD8+ lymphocyte values was not satisfactory, because simulated numbers of these cells increased even at later stages of infection, when no further increase was observed in infected individuals. Modifications of the model were attempted to obtain better simulation results assuming the influence of HIV infection on CD8+ lymphocyte maturation. Satisfactory results were obtained, if the influx of immature CD4+ and CD8+ lymphocytes was constrained by HIV infection. This modified version was then used for simulation of the anti-CD8 antibody administration effect in HIV-infected persons.

• MeSH
• CD8-Positive T-Lymphocytes immunology   MeSH
• HIV Infections immunology   MeSH
• Humans MeSH
• Mathematical Computing * MeSH
• Models, Immunological * MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern-Gouy-Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.

• Keywords
• Double layer, Electric charge, Electromigration, Electroneutrality, Poisson equation,
• MeSH
• Electric Conductivity MeSH
• Electrolytes * MeSH
• Ions MeSH
• Solutions MeSH
• Models, Theoretical * MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Names of Substances
• Electrolytes * MeSH
• Ions MeSH
• Solutions MeSH