Modeling of Subsurface Biobarrier Formation

Biofilm-forming microbes can form biobarriers to inhibit contaminant migration in groundwater and potentially biotransform organic contaminants to less harmful forms. Biofilm-forming microbes thereby provide an in situ method for treatment of contaminated groundwater. A mathematical and numerical model to describe the population distribution and growth of bacteria in porous media is presented here. The model is based on the convection-dispersion equation with nonlinear reaction terms. Accurate numerical simulations are crucial to the development of contaminant remediation strategies. We use the nonstandard numerical approach that is based on non-local treatment of nonlinear reactions and modified characteristic derivatives. This approach leads to significant qualitative improvements in the behavior of the numerical solution. Numerical results for a simple biobarrier formation model are presented to demonstrate the performance of the proposed new method. Comparisons of simulated results with experimental results obtained from the Montana State Center for Biofilm Engineering are also presented

Understanding the Fundamental Molecular Mechanism of Osteogenic Differentiation from Mesenchymal Stem Cells

A mathematical model is presented to study the regulatory effects of growth factors in osteoblastogenesis. The model incorporates the interactions among mesenchymal stem cells, osteoblasts, and growth factors. The resulting system of nonlinear ordinary differential equations is studied analytically and numerically. Mathematical conditions for successful osteogenic differentiation and optimal osteoblasts population are formulated, which can be used in practice to accelerate bone formation. Numerical simulations are also presented to support the theoretical results and to explore different medical interventions to enhance osteoblastogenesis

Mathematical modeling of bioremediation of trichloroethylene in aquifers

AbstractTrichloroethylene (TCE) is a very common contaminant of groundwater. It is used as an industrial solvent and is frequently poured into the soil. There exist bacteria that can degrade TCE. In contrast with most cases of bioremediation, the bacteria that degrade TCE do not use it as a carbon source. Instead the bacteria produce an enzyme to metabolize methane. This enzyme can degrade other organics including TCE. In this paper we model in situ bioremediation of TCE in an aquifer by using two species of bacteria: one that forms biobarriers to restrict the movement of TCE and the second one to reduce TCE. The model includes flow of water, transport of TCE and the nutrients, bacterial growth and degradation of TCE. Nonstandard numerical methods are used to discretize the equations. Some results are presented

A Cellular Automata Model of Infection Control on Medical Implants

S. epidermidis infections on medically implanted devices are a common problem in modern medicine due to the abundance of the bacteria. Once inside the body, S. epidermidis gather in communities called biofilms and can become extremely hard to eradicate, causing the patient serious complications. We simulate the complex S. epidermidis-Neutrophils interactions in order to determine the optimum conditions for the immune system to be able to contain the infection and avoid implant rejection. Our cellular automata model can also be used as a tool for determining the optimal amount of antibiotics for combating biofilm formation on medical implants

Constructing One-Dimensional Continuous Models from Two-Dimensional Discrete Models of Medical Implants

Medically implanted devices are becoming increasingly important in medical practice. Over 4 million people in the United States have long-term biomedical implants. However, many medical implants have to be removed because of infection or because their protein coating causes excessive inflammation and decrease in the immune system response. In this work, a discrete two-dimensional model of blood cells and bacteria interactions on the surface of a medical implant is transformed into a discrete one-dimensional model. This one-dimensional model is then upscaled into a partial differential equation model. The results from the discrete two-dimensional model and the continuous one-dimensional model are then compared for different protein coating mixtures. Two medical treatment alternatives are also explored and the two models are compared again

(R1504) Second-order Modified Nonstandard Runge-Kutta and Theta Methods for One-dimensional Autonomous Differential Equations

Nonstandard finite difference methods (NSFD) are used in physical sciences to approximate solutions of ordinary differential equations whose analytical solution cannot be computed. Traditional NSFD methods are elementary stable but usually only have first order accuracy. In this paper, we introduce two new classes of numerical methods that are of second order accuracy and elementary stable. The methods are modified versions of the nonstandard two-stage explicit Runge-Kutta methods and the nonstandard one-stage theta methods with a specific form of the nonstandard denominator function. Theoretical analysis of the stability and accuracy of both modified NSFD methods is presented. Numerical simulations that concur with the theoretical findings are also presented, which demonstrate the computational advantages of the proposed new modified nonstandard finite difference methods

A simple model of immune and muscle cell crosstalk during muscle regeneration

Muscle injury during aging predisposes skeletal muscles to increased damage due to reduced regenerative capacity. Some of the common causes of muscle injury are strains, while other causes are more complex muscle myopathies and other illnesses, and even excessive exercise can lead to muscle damage. We develop a new mathematical model based on ordinary differential equations of muscle regeneration. It includes the interactions between the immune system, healthy and damaged myonuclei as well as satellite cells. Our new mathematical model expands beyond previous ones by accounting for 21 specific parameters, including those parameters that deal with the interactions between the damaged and dead myonuclei, the immune system, and the satellite cells. An important assumption of our model is the replacement of only damaged parts of the muscle fibers and the dead myonuclei. We conduce systematic sensitivity analysis to determine which parameters have larger effects on the model and therefore are more influential for the muscle regeneration process. We propose additional validation for these parameters. We further demonstrate that these simulations are species-, muscle-, and age-dependent. In addition, the knowledge of these parameters and their interactions, may suggest targeting or selecting these interactions for treatments that accelerate the muscle regeneration process

Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer

Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca2+ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca2+ and cell proliferation. This intracellular Ca2+ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs