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PubMed2005

Mathematically modelling the effects of counting factor in Dictyostelium discoideum.

Size regulation is a crucial feature in many biological systems, with misregulation leading to dysplasia or hyperplasia. The recent discovery of counting factor (CF) in Dictyostelium discoideum will lead to a greater understanding of how the system regulates the size of a group of cells. In this paper we mathematically model the known effects of CF using two different models: a cellular automata model and a discrete continuum hybrid model. With the use of these models we are able to understand how modulation of adhesion and motile forces by CF can facilitate stream breakup. In addition, the modelling suggests a new possible mechanism for stream breakup involving the frequency of cell reorientation.

Animals↗
PubMed2005

The course of tissue permeabilization studied on a mathematical model of a subcutaneous tumor in small animals.

One of the ways to potentiate antitumor effectiveness of chemotherapeutic drugs is by local application of short intense electric pulses. This causes an increase of the cell membrane permeability and is called electropermeabilization. In order to study the course of tissue permeabilization of a subcutaneous tumor in small animals, a mathematical model was built with the commercial program EMAS, which uses the finite element method. The model is based on the tissue specific conductivity values found in literature, experimentally determined electric field threshold values of reversible and irreversible tissue permeabilization, and conductivity changes in the tissues. The results obtained with the model were then compared to experimental results from the treatment of subcutaneous tumors in mice and a good agreement was obtained. Our results and the reversible and irreversible thresholds used coincide well with the effectiveness of the electrochemotherapy in real tumors where experiments show antitumor effectiveness for amplitudes higher than 900 V/cm ratio and pronounced antitumor effects at 1300 V/cm ratio.

Animals↗
PubMed1996

A mathematical model of cytosolic calcium dynamics in human umbilical vein endothelial cells.

Important among the responses of endothelial cells are cytosolic free calcium transients. These transients are mediated by several factors, including blood-borne agonists, extracellular calcium, and fluid-imposed shear forces. The transients are characterized by a rapid rise followed by a plateau phase. A base mathematical model is presented that reasonably reproduces the measured calcium transient in cultured human umbilical vein endothelial cells responding to thrombin. Kinetic equations for receptor activation and calcium mobilization comprise the model. A graded response of intracellular free calcium to increasing concentrations of agonist is predicted. Also predicted is the elevation of the peak value and the plateau level by steady nonspecific leak of calcium across the plasma membrane. The influences of capacitative calcium entry, calcium-induced calcium release, and buffering by cytosolic proteins are investigated parametrically. The model predicts significant depletion of cellular calcium in response to agonist stimulation.

Buffers↗
PubMed2004

Barotrauma during air travel: predictions of a mathematical model.

Middle ear barotrauma during flight is a painful disorder experienced by passengers who cannot properly regulate their middle ear pressure in response to the changing cabin pressures during ascent and descent. Previous reports emphasized the important role of poor eustachian tube function in disease pathogenesis but paid little attention to other moderating factors. Here we describe a mathematical model of middle ear pressure regulation and simulate the pressure response to the changes in cabin pressure experienced over typical flights. The results document buffering mechanisms that decrease the requisite efficiency of active, muscle-assisted eustachian tube opening for disease-free flight. These include the relative difference between destination and departure elevations and the ratio of maximum tympanic membrane volume displacement to middle ear volume, where greater absolute values require lesser efficiencies for disease-free flight. Also, the specific type of functional deficit is important since ears with a completely obstructed eustachian tube can be less susceptible to barotrauma than those with a eustachian tube that passively opens but fails to dilate in response to muscle activity. These buffering systems can explain why some children and adults with poor eustachian tube function do not experience middle ear barotrauma.

Aircraft↗
PubMed2001

Macrofilaricides and onchocerciasis control, mathematical modelling of the prospects for elimination.

BACKGROUND: In most endemic parts of the world, onchocerciasis (river blindness) control relies, or will soon rely, exclusively on mass treatment with the microfilaricide ivermectin. Worldwide eradication of the parasite by means of this drug is unlikely. Macrofilaricidal drugs are currently being developed for human use. METHODS: We used ONCHOSIM, a microsimulation mathematical model of the dynamics of onchocerciasis transmission, to explore the potentials of a hypothetical macrofilaricidal drug for the elimination of onchocerciasis under different epidemiological conditions, as characterized by previous intervention strategies, vectorial capacity and levels of coverage. RESULTS: With a high vector biting rate and poor coverage, a very effective macrofilaricide would appear to have a substantially higher potential for achieving elimination of the parasite than does ivermectin. CONCLUSIONS: Macrofilaricides have a substantially higher potential for achieving onchocerciasis elimination than ivermectin, but high coverage levels are still key. When these drugs become available, onchocerciasis elimination strategies should be reconsidered. In view of the impact of control efforts preceding the introduction of macrofilaricides on the success of elimination, it is important to sustain current control efforts.

Animals↗
PubMed2000

A mathematical model of cerebral perfusion subjected to Gz acceleration.

BACKGROUND: When the human body is exposed to a high gravitational load, the blood supply to the brain is reduced and loss of consciousness may occur. Our goal is to identify the principal mechanical causes of reduced blood supply to the brain during high +Gz. METHODS: We have developed a mathematical model to investigate the influence of Gz on the cerebral circulation. Blood flow is modeled using a one-dimensional flow approximation, in which the cross-sectional area of elastic vessels is determined as a non-linear function of the transmural (blood minus external) pressure. The intracranial vessels are subjected to cerebrospinal fluid pressure (PCSF) which is determined from the condition that the cranial volume is conserved. RESULTS: For a constant pressure difference of 100 mm Hg applied to the arterial and venous ends of the model, blood flow is diminished for +Gz. At approximately +5 G, the blood flow predicted by the model is insufficient to maintain normal functioning of the brain. PCSF is approximately equal to the blood pressure in the large intracranial veins for all values of Gz. Extracranial arteries and the intracranial vessels do not collapse, even when Gz is substantially higher than normal. However, the extracranial veins are collapsed even for moderate +Gz. CONCLUSIONS: Even if cardiac output is maintained at normal levels, cerebral perfusion will fall because of the increasing resistance of the cerebral flow circuit. This increase is largely due to the collapse of the extracranial veins, which begins at moderate Gz and becomes dominant at a Gz of approximately 4.5.

Adaptation, Physiological↗
PubMed2004

Mathematical model for describing reactions of residual chlorine with organic matter in reclaimed wastewater.

Among several applications of urban wastewater reuse, use of reclaimed wastewater to sustain stream flows has become attractive in the urban area. Since these rivers are used for recreational purposes and for restoring aquatic eco-system, the adequate control of residual chlorine is essential. Mathematical model for describing reactions between residual chlorine and organic matter in reclaimed wastewater has been developed. The model considers the effect of molecular weight distribution of organic matter on the reaction rate. Lab-scale experiments were performed to estimate reaction rates constants and to examine their temperature dependency. The experiments showed that 1) the smaller organic matter gave the larger reaction rate; 2) temperature effect on reaction rate was described by the Arrhenius formula; 3) decline of free chlorine had more temperature dependency than combined chlorine. The comparison of computed results with data from lab-scale experiments confirmed the validity of the model. We used the one-dimensional dispersion model with proposed reaction model and examined the seasonal variation of residual chlorine profile along the river sustained by reclaimed wastewater in Sapporo. Simulation showed that seasonal variation of nitrification performance in secondary treatment as well as change in temperature caused seasonal variation in residual chlorine profile along the river.

Chlorine Compounds↗
PubMed2005

Mathematical modelling of in situ and in vitro efflux of ciprofloxacin and grepafloxacin.

The efflux process due to p-glycoprotein-like mechanisms of ciprofloxacin (CIP) and grepafloxacin (GRX) has been studied "in situ" in rats and "in vitro" in Caco-2 cells. The results were modelled by a curve fitting procedure which allowed the characterization of the passive (Pd) and carrier mediated parameters (Vm and Km) from the raw data without initial velocities estimation. CIP absorption in rat was characterized as a passive diffusion at the assayed concentrations. Although the involvement of an efflux transporter cannot be ruled out, its relevance in the transport of the fluoroquinolone is negligible. In GRX absorption, an efflux process is implicated and it is detected in both absorption models. GRX permeability depends on the intestinal segment, reflecting the previously reported different expression level of the efflux transporters along the gut in rat. A first attempt to correlate the "in vitro" and the "in situ" data has been done. The mathematical model has been constructed using very simplistic assumptions and it will require further refinement but, nevertheless, the results are promising and demonstrate that a good modelling approach helps to identify the system critical parameters and how the system behaviour change when the parameters are modified as it happens when we move from the "in vitro" to the "in situ" level. Predicted versus experimental permeability values show a good correlation, demonstrating that the relevance of the secretion process "in situ" in rat can be predicted from the "in vitro" cell results.

Animals↗
PubMed2001

A mathematical model for quorum sensing in Pseudomonas aeruginosa.

The bacteria Pseudomonas aeruginosa use the size and density of their colonies to regulate the production of a large variety of substances, including toxins. This phenomenon, called quorum sensing, apparently enables colonies to grow to sufficient size undetected by the immune system of the host organism. In this paper, we present a mathematical model of quorum sensing in P. aeruginosa that is based on the known biochemistry of regulation of the autoinducer that is crucial to this signalling mechanism. Using this model we show that quorum sensing works because of a biochemical switch between two stable steady solutions, one with low levels of autoinducer and one with high levels of autoinducer.

Bacterial Proteins↗
PubMedDate not supplied

The seasonal pattern of dengue in endemic areas: mathematical models of mechanisms.

In dengue-endemic areas such as Thailand, there is clear seasonality in the number of reported cases of dengue virus disease. However, the roles of different entomological and biological variables in determining this pattern have not been ascertained. To investigate this, seasonally-varying parameters were introduced in a step-wise fashion into a mathematical model of the transmission dynamics of dengue viruses. The predicted prevalence of infection was then compared to observed seasonal patterns of disease. The strongest influences on the pattern of infection and its seasonal variation were duration of infectiousness of the host, vector mortality, and biting rate. However, seasonally-varying parameters such as the latent period of infection in the vector had to be incorporated into the model to generate the correct timing of peak infection prevalence. A few limiting variables usually control the prevalence of an infectious disease because small changes in their values can carry the infection beyond the threshold at which its basic reproductive number is one. It was changes in such parameters (vector biting and mortality rate) which caused seasonal prevalence, but the timing of peak prevalence was a result of time delays within the system.

Dengue↗
PubMedDate not supplied

A mathematical model for comparison of bolus injection, continuous infusion, and liposomal delivery of doxorubicin to tumor cells.

Determining the optimal mode of delivery for doxorubicin is important given the wide use of the drug against many tumor types. The relative performances of bolus injection, continuous infusion, liposomal and thermoliposomal delivery are not yet definitely established from clinical trials. Here, a mathematical model is used to compare bolus injection, continuous infusion for various durations, liposomal and thermoliposomal delivery of doxorubicin. Effects of the relatively slow rate, and saturability, of doxorubicin uptake by cells are included. Peak concentrations attained in tumor cells are predicted and used as a measure of antitumor effectiveness. To measure toxicity, plasma area under the curve (AUC) and peak plasma concentrations of free doxorubicin are computed. For continuous infusion, the duration of infusion significantly affects predicted outcome. The optimal infusion duration increases with dose, and is in the range 1 to 3 hours at typical doses. The simulations suggest that continuous infusion for optimal durations is superior to the other protocols. Nonthermosensitive liposomes approach the efficacy of continuous infusion only if they release drug at optimal rates. Predictions for thermosensitive liposomes indicate a potential advantage at some doses, but only if hyperthermia is applied locally so that the blood is not significantly heated.

Antineoplastic Agents↗
PubMed2002

A mathematical model of post-canalization thrombolysis.

During the initial phase of lysis of an occlusive thrombus using lytic agents such as tissue plasminogen activator, blood flow through the centre of the clot is established (the process of recanalization). Following canalization, the clot remains on the vessel wall and further lysis is required. This paper develops a multi-species mathematical model to describe the bulk chemical reactions in the bloodstream and the convective and diffusive transport of chemical species to and from the clot surface in conditions following canalization. For the steady state case, the model indicates that the process of clot lysis following initial recanalization is dominated by surface chemical reactions and the bulk reactions play little role in the lytic process. Lytic rate is dependent on the clot geometry and flow conditions. The rate of clot dissolution is greatest at the upstream end of the clot and decreases steadily downstream due to lytic agent being removed from the flowing blood as it binds to the clot surface. This model may be further developed and used to simulate and compare different lytic regimes.

Animals↗
PubMed2001

Mathematical modeling of carbon monoxide exposures from anesthetic breakdown: effect of subject size, hematocrit, fraction of inspired oxygen, and quantity of carbon monoxide.

BACKGROUND: Carbon monoxide (CO) is produced by reaction of isoflurane, enflurane, and desflurane in desiccated carbon dioxide absorbents. The inspiratory CO concentration depends on the dryness and identity of the absorbent and anesthetic. The adaptation of existing mathematical models to a rebreathing circuit allows identification of patient factors that predispose to more severe exposures, as identified by carboxyhemoglobin concentration. METHODS: From our companion study, the authors used quantitative in vitro CO production data for 60 min at 7.5% desflurane or 1.5% isoflurane at 1 l/min fresh gas flow. The carboxyhemoglobin concentration was calculated by iteratively solving the Coburn Forster Kane equation modified for a rebreathing system that incorporates the removal of CO by patient absorption. Demonstrating good fit of predicted carboxyhemoglobin concentrations to published data from animal and human exposures validated the model. Carboxyhemoglobin concentrations were predicted for exposures of various severity, patients of different sizes, hematocrit, and fraction of inspired oxygen. RESULTS: The calculated carboxyhemoglobin concentrations closely predicted the experimental results of other investigators, thereby validating the model. These equations indicate the severity of CO poisoning is inversely related to the hemoglobin quantity of a subject. Fraction of inspired oxygen had the greatest effect in patients of small size with low hematocrit values, where equilibrium and not the rate of uptake determined carboxyhemoglobin concentrations. CONCLUSION: This model predicts that patients with low hemoglobin quantities will have more severe CO exposures based on the attainment of a higher carboxyhemoglobin concentration. This includes patients of small size (pediatric population) and patients with anemia.

Anesthetics, Inhalation↗
PubMedDate not supplied

[Chronoinotropic reaction of the hypertrophied myocardium using an electromechanical coupling mathematical model].

Static and dynamic chrono-inotropic responses were recorded from both normal and hypertrophic rat auricular myocardium. The slope of the static force-frequency relation from hypertrophied heart was steeper than in the control hearts. The cellular mechanisms underlying changes in the force frequency response associated with hypertrophy of the heart were studied by means of a mathematical model of excitation-contraction coupling. The characteristic features of hypertrophied heart force-frequency relations are shown to be due to the enhanced volume of the intracellular Ca-stores in contrast to the total volume of the cardiomyocyte.

Animals↗
PubMed1990

[A mathematical model of membrane ion transport in psoriasis].

The authors discuss the problems related to mathematical simulation of ionic transport via cellular membrane and to identification of such models as exemplified by calcium metabolism. The examined model adequately reflects the characteristic features of the time course of ion transport in various stages of psoriasis, this permitting the use of this model in mathematical solving of the problem of optimal treatment of psoriasis patients. Graphs and results of estimations made with personal IBM-compatible computer are presented.

Biological Transport↗
PubMedDate not supplied

A mathematical model of continuous arterio-venous hemodiafiltration (CAVHD).

Continuous arterio-venous hemodiafiltration (CAVHD) differs from conventional hemofiltration and dialysis by the interaction of convection and diffusion, the use of very low dialysate flow rates and by the deterioration of membrane conditions during the treatment. In order to study the impact of these phenomena on diffusive transport, we developed a mathematical model of the kinetics of CAVHD solute transport from plasma water to dialysate. The model yields an expression of the diffusive mass transfer coefficient, Kd, as a function of blood, filtrate and dialysate flow rates and solute concentrations, which can be measured in the clinical setting. This paper gives a description of the model derivation. Kd is demonstrated to vary depending on dialysate flow and duration of treatment.

Blood Flow Velocity↗
PubMed2004

Nonequilibrium capillary electrophoresis of equilibrium mixtures, mathematical model.

We recently introduced a new electrophoretic method, nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM). NECEEM provides a unique way of finding kinetic and equilibrium parameters of the formation of intermolecular complexes from a single electropherogram and allows for the use of weak affinity probes in protein quantitation. In this work, we study theoretical bases of NECEEM by developing a mathematical model for the new method. By solving a system of partial differential equations with diffusion in linear approximation, we found the analytical solution for concentrations of components involved in complex formation as functions of time from the beginning of separation and position in the capillary. The nonnumerical nature of the solution makes it a powerful tool in studying the theoretical foundations of the NECEEM method and modeling experimental results. We demonstrate the use of the model for finding binding parameters of complex formation by nonlinear regression of NECEEM electropherograms obtained experimentally.

DNA↗
PubMed1983

A mathematical model of particle retention in the air-spaces of human lungs.

Knowledge of the total and regional lung retention of particles inhaled continuously by man over long periods can be useful in understanding the potential role of inhaled particles in the pathogenesis of lung diseases. Owing to practical and ethical considerations, however, little or no experimental information exists. A mathematical model of particle retention simulating environmental and occupational exposures has therefore been developed that takes into account particle deposition, tracheobronchial clearance, and two phases of alveolar clearance in the Weibel A anatomical lung model. The derived equations of retention kinetics predict retention of particles as a function of exposure time. For a continuous exposure (simulating environmental conditions) to 4 microns particles, the model predicts that retained particles approach an equilibrium between deposited and cleared particles with the 95% level being reached in 293 days. For an intermittent exposure (simulating occupational conditions) equilibrium is approached in five years. The whole lung burden of particles is predicted to be 9% of the total mass that entered the lung after a one-year environmental exposure and 1.5% after a 25-year occupational exposure. The equilibrium surface concentration and integrated dose of particles per airway generation predict enhanced risk to the pathogenic effects of inhaled particles in the large airways and respiratory bronchioles.

Air Pollution↗

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