Mathematical modeling of cancer radiovirotherapy

Cancer virotherapy represents a dynamical system that requires mathematical modeling for complete understanding of the outcomes. The combination of virotherapy with radiation (radiovirotherapy) has been recently shown to successfully eliminate tumors when virotherapy alone failed. However, it introduces a new level of complexity. We have developed a mathematical model, based on population dynamics, that captures the essential elements of radiovirotherapy. The existence of corresponding equilibrium points related to complete cure, partial cure, and therapy failure is proved and discussed. The parameters of the model were estimated by fitting to experimental data. By using simulations we analyzed the influence of parameters that describe the interaction between virus and tumor cell on the outcome of the therapy. Furthermore, we evaluated relevant therapeutic scenarios for radiovirotherapy, and offered elements for optimization.     

Mathematical modeling of planar polarity

Although it is well established that the Frizzled receptor is involved in the transmission of polarity information from cell to cell in the Drosophila cuticle, its precise role is still unclear. A recent paper by presents a mathematical model of a feedback loop-based mechanism for propagation of polarity between cells that can account for the known functions of Frizzled.     

Mathematical modeling of tumor-induced angiogenesis

Journal of Mathematical Biology -     

Mathematical modeling of capillary density

Capillary density is important as a determinant for total oxygen transport to tissue. Because both capillary morphology and fiber composition vary considerably from muscle to muscle, measurement of capillary morphology and fiber composition vary considerably from muscle to muscle, measurement of capillary density alone cannot provide the detailed information necessary for analyzing physical phenomena. In this report we consider the capillary:fiber ratio, fiber types, fiber diameters, and fiber composition as components of a unit to express capillary density. We have applied the hexagonal fiber array model to calculate capillary density in cat and dog striated muscle and compared this with experimental data in the literature. The results indicate that this model may be useful for predicting capillary densities from simple biopsy procedures.     

Mathematical modeling of hyphal tip growth

The mathematical modelling of growing filamentous cells has been approached in a variety of ways ranging from simple geometric to biomechanically based models using exact, nonlinear, elasticity theory for shells and membranes in which a growth mechanism is included, and alternative approaches using visco-plasticity theory. We describe how the nonlinear elastic model is able to capture essential biomechanical mechanical features of the growth of a broad array of filamentous cells including fungi, actinomycetes, pollen tubes, and root hairs. A comparison between this approach and visco-plasticity based models is made.     

Mathematical modeling and optimization of plasmadiafiltration

A mathematical model of mass transport of toxic substances with small, middle and large molecules weight in the body compartments and in the extracorporal system was worked out and used in the clinic for individual optimization and prediction of final results when treating patients with acute hepatic and renal failure in plasmadiafiltration. Permeability and the sieving coefficients were found "in vivo" in the plasma for 3 types of dialysers with different membranes. For practical use of this model a program was written by an interactive dialogue for the personal computer.     

Mathematical modeling of affinity ultrafiltration process

An affinity ultrafiltration process has been developed by exploiting affinity binding in conjunction with cross-flow filtration. The process was proven to possess high resolution, high recovery yield, and ease of scale-up. The process could purify trypsin from a trypsin-chymotrypsin mixture batchwise or continuously. Essential for applying this concept was the synthesis of a water-soluble high-molecular-weight polymer bearing m-aminobenzamidine, a strong and specific trypsin in hibitor. A mathematical model was also developed to describe the dynamic behavior of the newly developed purification process. The model was able to predict the profiles of enzyme concentrations in the process with high accuracy.     

植物自毒物质剂量与效应的机理模型研究

植物自毒现象在自然和农业生态系统中广泛存在.该研究针对植物自毒作用强弱与自毒物质浓度相关的低促高抑赫米斯(Hormesis)特性,在An-Johnson-Lovett Hormesis模型中引入生态限制因子米式(Mitscherlich)模型,建立了自毒物质作用的剂量/自毒效应规律的机理数学模型.模型的演示与文献的报道结果一致,用已经发表的多种植物的自毒研究数据进行检验显示很强的拟合效果,说明以生态限制因子为核心建立的自毒模型不仅从植物生长的生物生态学属性上进一步揭示了自毒作用随自毒物质浓度变化的效应规律,同时在应用上具普遍性,这为今后更深入地研究自毒作用提供了一理论平台.     

Mathematical modeling of metabolism and hemodynamics

We provide a mathematical study of a model of energy metabolism and hemodynamics of glioma allowing a better understanding of metabolic modifications leading to anaplastic transformation from low grade glioma. This mathematical analysis allows ultimately to unveil the solution to a viability problem which seems quite pertinent for applications to medecine.     

Mathematical modeling of T-cell activation kinetic

T-cell activation is a crucial step in mounting of the immune response. The dynamics of T-cell receptor (TCR) specific recognition of peptide presented by major histocompatibility complex (MHC) molecule decides the fate of the T cell. Several biochemical interactions interfere resulting in a highly complex mechanism that would be difficult to understand without computer help. The aim of the present study was to define a mathematical model in order to approach the kinetics of monoclonal T-cell-specific activation. The reaction scheme was first described and the model was tested using experimental parameters from the published data. Simulations were concordant with experimental data showing proportional decrease of membrane TCR and production of interleukin-2 (IL-2). Agonist and antagonist peptides induce different levels of intracellular signal that could make the yes or no decision for entry to cell cycle. Different conditions (peptide concentrations, initial TCR density and exogenous IL-2 levels) can be tested. Several parameters are missing for parameters estimation and adjustment before it could be adapted for a polyclonal T-cell reaction model. However, the model should be of interest in setting experiments, simulation of clinical responses and optimization of preventive or therapeutic immunotherapy.     

Mathematical modeling of production of microbial lipids

In the microbial lipid production system using the yeast Rhodotorula gracilis, CFR-1, kinetics of lipid accumulation and substrate utilisation at initial substrate concentrations in the range of 20–100 kg/m³ were investigated using shake flask experiments. A mathematical representation based on logistic model for biomass and Luedeking-Piret model for lipid accumulation gave reasonably good agreement between the theoretical and experimental values for substrate concentration less than 60 kg/m³. The kinetic expressions and parameters obtained through shake flask studies were directly applied to experiments in the laboratory fermentors also and the models were found to hold good for the prediction of the change of biomass, product as well as substrate with time. The attainment of a saturation in the intracellular lipid accumulation with time, however, was not predicted by the model which was shown to be an inherent feature of the Luedeking-Piret model.List of Symbols S ₀, P ₀ kg/m³ Initial concentrations of sugar and lipid respectively - S, S(t) kg/m³ Concentrations of sugar and lipid respeclively at any timet - p,p(t) L kg/m³ Maximum concentration of lipid produced - E % Maximum sugar utilised - dP/dt kg/(m³ · h) Rate of lipid production - -dS/dt kg/(m³ · h) Rate of sugar utilisation - _max h^–1 Maximum specific growth rate - X _max kg/m³ Maximum biomass reached in a run - P _max kg/m³ Maximum product concentration - m, n Constants used in Luedeking-Piret model in eq. (7) - , Constants used to predict residual sugar - k _e maintainance coefficient - Y _x g/g Biomass yield based on sugar consumed - Y _p g/g Lipid yield based on sugar consumed - (dP/d t)_stat kg/(m³ · h) Rate of lipid production at stationary phase - (dS/dt)_stat kg/(m³ · h) Rate of sugar utilisation at stationary phase     

Mathematical modeling of production of microbial lipids

As a part of the investigations on the microbial lipid production using the yeast Rhodotorula gracilis, CFR-1, kinetics of the biomass synthesis has been studied using shake flask experiments. Using a medium containing a carbon to nitrogen ratio of 701, the rates of biomass production were followed at different initial substrate concentrations in the range of 20–100 kg/m³. A logistic model was found to be reasonably adequate to describe the kinetics of the growth of biomass; the maximum specific growth rate of 0.105 h^–1 was applicable for substrate concentrations less than 60 kg/m³, which gave reasonable agreement between predicted and actual biomass concentration values.List of Symbols S ₀, X ₀ kg/m³ Initial concentrations of sugar, non lipid biomass respectively - X, X(t) kg/m³ Concentrations of non lipid biomass at any time t - dX/dt kg/(m³ · h) Rate of biomass growth - h^–1 Specific growth rate - _max h^–1 Maximum specific growth rate - K _s mol/dm³ Monods constant - X _max kg/m³ Maximum biomass reached in a run     

Mathematical modeling of pathogenicity of Cryptococcus neoformans

Cryptococcus neoformans (Cn) is the most common cause of fungal meningitis worldwide. In infected patients, growth of the fungus can occur within the phagolysosome of phagocytic cells, especially in non‐activated macrophages of immunocompromised subjects. Since this environment is characteristically acidic, Cn must adapt to low pH to survive and efficiently cause disease. In the present work, we designed, tested, and experimentally validated a theoretical model of the sphingolipid biochemical pathway in Cn under acidic conditions. Simulations of metabolic fluxes and enzyme deletions or downregulation led to predictions that show good agreement with experimental results generated post hoc and reconcile intuitively puzzling results. This study demonstrates how biochemical modeling can yield testable predictions and aid our understanding of fungal pathogenesis through the design and computational simulation of hypothetical experiments.     

Mathematical foundations for modeling poikilotherm mortality

A mathematical basis for incorporating mortality into models of insect development is presented. There has been much attention given to modeling insect development, but the quantitative treatment of mortality, especially of immature stages, is often overlooked. This paper investigates mortality as it affects immature-organism development, proceeding from the simple to the complex. The methods presented are illustrated with examples taken from boll-weevil immature mortality within cotton floral buds.     

Mathematical framework for modeling tissue growth

A phenomenological continuum mechanics framework for modeling growth of living tissues is proposed. Tissue is considered as an open system where mass is not conserved. The momentum balance is completed with the full-scale mass balance. Constitutive equations define simple growing materials. 'Thermoelastic' formulation of a simple growing material is specified. Within this framework traction free growth of a cylinder is considered. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to a boundary layer solution of the governing equations.     

Mathematical modeling of differentiation in dictyostelium discoideum

Methods for the dynamic analysis of biochemical differentiation are presented. These are demonstrated in the analysis of biochemical differentiation of the carbohydrate system in D. discoideum. Procedures for simplification which are presented are projection and contraction of the system trajectory in state space and the generation of reduced equivalent dynamic metabolic networks. The importance of the hierarchical structure of differentiating systems is discussed and the concept of a dynamic embedding diagram is introduced. It is shown that complex systems must be analyzed on an epoch by epoch basis, each epoch being a period of time characterized by a constant dynamic embedding diagram, and that widely different time scales and state space scales may be necessary in different epochs. In particular there is no a priori lower limit to the time scale which may be necessary during the analysis. Some problems in mathematically defining differentiation are discussed.     

Mathematical modeling of the hypothalamic-pituitary-adrenal system activity

Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans. The aim of this work was to explore in greater detail the role of this system in normal, homeostatic, conditions, since it is the first and unavoidable step in further understanding of the role of this complex neuroendocrine system in pathophysiological conditions. Neither the underlying mechanisms nor the physiological significance of this system are fully understood yet.