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PubMed1985

A mathematical model for the transport and fate of organic chemicals in unsaturated/saturated soils.

A mathematical model, simulating the transport and fate of nonionizable organic compounds in unsaturated/saturated porous media (soils) in a terrestrial microcosm has been developed. Using the principles of water mass, momentum, heat energy and chemical mass balance, the three fields: moisture, temperature, and liquid phase chemical concentration are solved for simultaneously by coupling the soil slab to an environmentally realistic air-soil interface (a dynamic free boundary) conditions and a prescribed height water table. The environmental conditions at the soil surface-air chamber interface are easily changed, via geometric scaling factors, to simulate either an open agricultural field or a landfill type of situation. Illustrative simulation runs examine the effects of different soil-chemical characteristics on hydrological and chemical concentration profiles.

Biodegradation, Environmental↗
PubMed2003

A mathematical model of phytoremediation for petroleum-contaminated soil: model development.

We present a simple model for root length density that combines the generally accepted spatial (exponential decrease with depth) and temporal (sinusoidal) variability of root length. Parameters in this model for root length density can be determined from assumed or measured information regarding the annual biomass turnover, maximum standing biomass, and maximum depth of root penetration. The root length density model, coupled with information regarding the average root lifespan, gives specific root growth and senescence functions that are the forcing functions for the phytoremediation model. We present a screening level mathematical model for phytoremediation that accounts for the growth and senescence of roots in the system. This is an important factor for recalcitrant, immobile compounds found in weathered crude oil contaminated soils. The phytoremediation model is based on variable volume compartments that have individual first-order degradation rate constants; as the roots move through the soil, the soil cycles through the rhizosphere zone, decaying root zone and bulk soil zone. Thus, although the oil is immobile, as the roots penetrate through the soil the oil is brought into contact with the rhizosphere.

Algorithms↗
PubMed1993

[Comparison of the transmission dynamics and the control effects between malaria and filariasis by using mathematical model].

By dynamic modeling based on Ross & MacDonald's mathematical model, the characteristics of rapid transmission of malaria and slow transmission of filariasis was compared. The dynamic mechanism showed that the infection efficiency in filariasis, namely, the probability of becoming infected in man by one infective bite of mosquito, was much lower than that in malaria; hence the vectorial capacity or transmission velocity in filariasis was also markedly lower than that in malaria. Since the intensity of infection i.e. the microfilaria density can largely affect the infection efficiency in filariasis, drug treatment, especially using DEC-medicated salt can reduce the intensity of infection and the infection efficiency, thus interrupting transmission finally. However, for malaria, only when the measures for mosquito vector control (including mosquito proofing) are taken as a priority to reduce the vectorial capacity or transmission velocity, malaria can then be controlled subsequently. These theoretical analyses are being demonstrated by the practice for malaria and filariasis control in our country, which could also be used as a theoretical base for enlightening the successful filariasis control strategies in our country.

Animals↗
PubMed1991

A mathematical model for calculating the vector magnetic field of a single muscle fiber.

A mathematical model is described for calculating the volume-conducted magnetic field from active muscle fibers in an anisotropic bundle. With earlier models, the azimuthal magnetic field of a nerve bundle was calculated and the results were compared with the fields measured by toroidal pickup coils. The present model is capable of evaluating all three of the magnetic field components and is thus applicable for analyzing SQUID magnetometer recordings of fields from a muscle bundle. The component of the magnetic field parallel to the fiber axis is more than an order of magnitude smaller than either of the other two components. The amplitude of the magnetic signal is strongly dependent upon the anisotropy of the muscle bundle, the intracellular conductivity, the radius of the muscle fiber, the radius of the muscle bundle, and the location of the fiber in the muscle bundle. The peak-to-peak amplitude of the single-muscle-fiber action field increases linearly with increasing intracellular conductivity, as the square of the radius of the muscle fiber, and exponentially with the distance between the location of the fiber and the center of the bundle.

Action Potentials↗
PubMed1976

A mathematical model of the chemotherapeutic treatment of acute myeloblastic leukemia.

Based on our previous mathematical model of the acute myeloblastic leukemic (AML) state in man, we superimpose a chemotherapeutic drug treatment regimen. Our calculations suggest that small changes in the protocol can have significant effects on the result of treatment. Thus, the optimal period between drug doses is the S-phase interval of the leukemic cells--about 20h--and the greater the number of doses administered in a given course treatment, the longer the rest interval should be before the next course is administered. For a patient with a "slow" growing AML cell population, remission can be achieved with one or two courses of treatment, and further suppression of the leukemic population can be achieved with continued courses of treatment. However, for patients with a "fast" growing AML cell population, a similar aggressive treatment regimen succeeds in achieving remission status only at the cost of very great toxic effects on the normal neutrophil population and its precursors.

Cytarabine↗
PubMed1995

Mathematical modelling in risk/exposure assessment of tobacco related lung cancer.

The existence of a dose-related increase of lung cancer risk in cigarette smokers has been indisputably established. This finding, however, is not confirmed at low doses (< 5 cigarettes/day), there still being a lack of epidemiological data. The use of mathematical models of carcinogenesis to extrapolate from higher doses allows estimation of the risk for very light smokers. The present study has been designed to compare a set of mathematical models, i.e. one-hit, two-stage, multi-stage, logit, probit, and Weibull, in extrapolating relative risks at low doses from the data of nine large cohort studies on cigarette smokers reported in the IARC Scientific Monograph on tobacco smoking. All models evaluated, apart from the one-hit, achieved a good fit, with the proportion of explained variance ranging between 61% and 67%. The relative risk estimates for passive smokers from the most updated epidemiological studies were taken into account to evaluate, on the basis of these models, the corresponding exposure in terms of 'cigarette equivalent' smoked. These values ranged from 0.21 to 0.43 cigarettes/day for the two-stage and multi-stage model, while probit, logit and Weibull models, yielded estimates one or even two orders of magnitude lower. The authors emphasize the substantial agreement between the estimates of 'cigarette equivalent' based on the application of two-stage and multi-stage models to the epidemiological evidence on the effect of passive smoking and to the data based on the comparison of tobacco metabolites in active and passive smokers.

Dose-Response Relationship, Drug↗
PubMed2005

Mathematical model of the rupture mechanism of intracranial saccular aneurysms through daughter aneurysm formation and growth.

OBJECTIVES: Daughter aneurysms have been strongly associated with saccular aneurysm rupture. We constructed a mathematical model to help explain this association as a possible hemodynamic mechanism for intracranial saccular aneurysm rupture. METHODS: Our model is based on the assumption that when an aneurysm reaches a state of imminent rupture, the weakest area of the aneurysm wall responds passively to a surge of intra-aneurysmal pressure by forming a daughter aneurysm that will be the site of the eventual rupture. The daughter and parent aneurysms were assumed to be spherical. Using mathematical modeling, the growth of the daughter aneurysm was observed. To obtain the change in tensile stress in the daughter aneurysm wall under constant pressure and changing geometry, the Law of Laplace was applied to the parent and the daughter aneurysms. RESULTS: The model reveals that the stress factor, i.e. tensile stress in the daughter aneurysm wall relative to the wall strength (rupture point), is dependent on two geometric parameters: the orifice factor (mu), which represents the relative size of the daughter aneurysm orifice radius to the parent aneurysm radius; and the aspect ratio (lambda), which represents the height-to-orifice ratio of the daughter aneurysm. As the daughter aneurysm develops, the stress factor first decreases to protect against rupture. Minimal stress is attained at an aspect ratio (lambda) of 0.577 regardless of the orifice factor. This is a relatively stable state. Further growth of the daughter aneurysm results in an increase of stress above the minimum, eventually leading to rupture at a stress factor of 1. A smaller orifice factor mu allows this aneurysm to grow to a higher aspect ratio lambda before rupture. DISCUSSION: Daughter aneurysm formation is a likely path to aneurysm rupture. The formation of a daughter aneurysm temporarily decreases the tensile stress within a parent aneurysm in which rupture is imminent, indicating a temporary protective role of daughter aneurysm development. Aneurysms harboring daughter aneurysms are at a more advanced stage of development, hence at a greater risk for rupture. The severity of the rupture risk can be estimated on the basis of daughter aneurysm geometry; aspect ratio lambda > 0.577 indicates a greater risk of rupture. Furthermore, daughter aneurysms with larger orifices are associated with a greater risk of rupture.

Aneurysm, Ruptured↗
PubMed1993

Use of a new mathematical model in fitting survivorship curves of Drosophila treated with the antioxidant thiazolidine carboxylic acid.

We have recently proposed a mathematical model of survival mortality kinetics. It is based on biological and statistical hypotheses and is able to fit survivorship curves even at advanced ages, where other models fail. The mathematical function contains two parameters, omega and So, related to deterministic and stochastic factors, respectively. In the present paper the model has been applied to a set of survival curves of Drosophila melanogaster. The different curves derived from populations of flies treated with different doses of the antioxidant thiazolidine carboxylic acid (TCA). The treatment induced a significant progressive increase of mean and maximum lifespan up to the TCA dietary concentration of 0.3%. Higher doses of TCA, on the contrary, were toxic, reducing both mean and maximum lifespan. An interpretation of the differential TCA effects has been attempted on the basis of the values assumed by the two model parameters.

Aging↗
PubMed2005

Mathematical models of oxygen and carbon dioxide storage and transport: the acid-base chemistry of blood.

This article describes a mathematical model of the acid-base chemistry of blood. The model is formulated from first principles by considering the "components" of blood and the reaction equations in the plasma and erythrocyte fractions. Equations are formulated to describe the total concentration of blood components, the physicochemical properties, and the equilibrium position of reactions. The model includes 28 equations and 12 parameters. All equations can be solved from six variables included in the model. The model uses simple mathematics, without introducing intermediate concepts or linear coefficients necessary for algebraic solution. Model equations are solved simultaneously using numerical methods. Model parameters are estimated and the model verified for plasma, fully oxygenated blood, and deoxygenated blood. Published data are used to estimate model parameters and normal conditions and to verify model simulations. The model reproduces experimental results, including addition or removal of CO2, or strong acid to plasma; CO2, strong acid or haemoglobin to blood; and the effects of deoxygenating blood. The model can also be used as the basis for models of whole body CO2 transport as illustrated in the accompanying article. As such, it is possible to simulate the effects on blood of physiological changes in ventilation or metabolism.

Acid-Base Equilibrium↗
PubMed2000

Mathematical modelling of the within-host dynamics of Plasmodium falciparum.

The development of malaria due to Plasmodium falciparum is a complex, multi-stage process. It is usually characterized by an exponential growth in the number of parasite-infected erythrocytes, followed by marked oscillations in this number with a period of 48 h, which are eventually dampened. This course of events has been the subject of various mathematical models. In this paper we propose a new mathematical model for the in-host asexual erythrocytic development of P. falciparum malaria. Synchronicity of the infection is shown to be an inherent feature of infection, irrespective of the duration of merozoite release from the liver. It will, therefore, cause periodic symptoms, as known in malaria patients. We also simulate the effects of an induced host immune response and show how the level of immunity affects the development of disease. The simulations fit well with the clinical observations. We show how infection can become asynchronous and discuss the effect of desynchronization on the circulating and total parasitaemia and demonstrate that synchronized broods will show parasitaemia fluctuations.

Animals↗
PubMed2003

Mathematical model to simulate the cellular dynamics of infection with human herpesvirus-6 in EBV-negative infectious mononucleosis.

Acute infection with human herpesvirus-6 induces physiological cell proliferation in persons without major immune deficiency. It thus can serve as a parameter to validate a mathematical model designed to simulate cell proliferation under physiological and pathological conditions. Such a mathematical model is presented to simulate various cell changes of the T-cell immune system during the course of HHV-6 infection. Model development follows several steps, beginning with a basic model containing physiological T-cell pools to the introduction of infectious stimuli in the final model. A search algorithm designed to optimize the system parameters, as well as initial variables of the model, is presented. The results of simulation runs for acute HHV-6 infection of the final computational model correspond well to the data, as documented in human patients; they suggest that the computational model presented for the simulation of T-cell levels in a given viral infection may well serve as a tool for similar studies of other viral infections, including those that lead to cellular aplasia or neoplasia.

Adolescent↗
PubMed1998

A mathematical model for micturition gives new insights into pressure measurement and function.

Our objective was to analyze the factors contributing to the development of detrusor pressure during micturition in the female with reference to a mathematical model. One hundred patients with predominantly stress incontinence were investigated with micturition pressure studies. Frictional and dynamic losses were estimated at various flow rates using a mathematical model. Almost 25% of patients recorded a micturition pressure below 11 cmH2O at peak flow (mean 23 cmH2O, range 0-91). Large inter- and intrapatient variations in micturition pressures were recorded on retesting. The low pressures were explained by a recently described external opening mechanism, backward stretching of the vagina during micturition by the muscles of the pelvic floor. This opened out the outflow tract and created the potential for a falsely high P(abd). The large variability in micturition pressures on retesting was attributed to changes in urethral radius being magnified to the fourth power. It was concluded that, micturition itself, and the components for pressure generation, are complex non-linear entities which appear to be greatly modified by the external striated pelvic floor opening mechanism. Addressing anatomical defects in this mechanism may be a fruitful route of future enquiry in females with emptying problems.

Adult↗
PubMed2000

Effect of mathematical modeling on the estimation of critical power.

PURPOSE: The purposes of this study were to re-examine the findings of previous studies by comparing the critical power (CP) estimates from five mathematical models and to determine the time to exhaustion during cycle ergometry at the lowest CP estimate from the five models. METHODS: Nine adult males performed a maximal incremental test to determine peak power and five or six randomly ordered trials on a cycle ergometer for the estimation of CP. Two linear, two nonlinear, and one exponential mathematical model were used to estimate CP. The subjects then completed two trials to exhaustion, or 60 min, at their lowest estimate of CP from the five models. RESULTS: The nonlinear three-parameter model (Nonlinear-3) produced a mean CP that was significantly (P < 0.05) less than the mean CP values derived from the other four models and was the lowest CP estimate for each subject. Two and three subjects, however, did not complete 60 min of cycling during the first and second trials at CP, respectively. At the end of the trials the subjects who completed 60 min of cycling had a mean heart rate of 92% of their maximum and a mean rating of perceived exertion of 17. CONCLUSION: These findings support previous studies that have indicated that in many cases CP overestimates the power output that can be maintained for at least 60 min.

Adult↗
PubMed2006

Listeria monocytogenes in multiple habitats and host populations: review of available data for mathematical modeling.

Listeria monocytogenes has the ability to survive and multiply in diverse habitats and to cause infection in a variety of animal species and humans. We evaluated the literature on survival and multiplication within and transmission among multiple host populations and habitats, including man, sewage, general environment (soil, water, and vegetation), silage (fermented plant material), animals (including wild and domestic animals), and food processing plants. The available knowledge on L. monocytogenes transmission dynamics was translated into the key process nodes of interrelated host- and habitat-specific mathematical models, providing a starting framework for future modeling work and the ultimate development of a system-wide model for evaluation of its transmission, and strategies to reduce human exposure. Because of the ability of L. monocytogenes to survive and multiply in many habitats and hosts, and the number of possible transmission routes, it is highly unlikely that it could be eradicated from any habitat or host, including man. However, L. monocytogenes load within and transmission among habitats and host populations could probably be reduced. Based on the published information, we hypothesize that three recent anthropogenic practices increase the load within and transmission among reviewed habitats and host populations: extended refrigerated storage of ready-to-eat foods allowing L. monocytogenes growth in foods that are contaminated during production or subsequent handling; feeding domestic ruminants with silage often contaminated with L. monocytogenes; and dispersal of contaminated products of sewage treatment to agricultural fields and waters. Future mathematical modeling work could test how much the reduction of L. monocytogenes load and transmission in hosts and habitats associated with these anthropogenic practices would reduce human exposure and consequently human listeriosis.

Animal Feed↗
PubMed2004

Coordination of cell growth and cell division: a mathematical modeling study.

Although there is general agreement that cell growth and division are functionally coordinated, the mechanisms that link the two processes are poorly understood. In this study, we have developed a mathematical model based on current biological concepts of the signaling transduction pathways involved in cell growth, which predicts that cell growth rate is proportional to cell surface area at birth. To investigate the relationship between growth control and cell division, we then applied our mathematical model to three classic experiments measuring cycle time versus cell birth size in fission yeast and Xenopus laevis, and the cell cycle delay in mammalian cells after serum withdrawal. When coupled to a cell cycle exhibiting 'sizer' and 'timer' phases, we show that a simple model in which growth rate is proportional to the cell surface area immediately after division reproduces the experimental observations including the relationship between cycle time and birth size in fission yeast and Xenopus laevis. The model also accounts for the cell cycle delay seen in restriction point experiments performed in HeLa cells.

Animals↗
PubMed1987

A mathematical model of the development of drug resistance to cancer chemotherapy.

A mathematical model incorporating descriptions of tumour growth kinetics and the effects of cytotoxic chemotherapy on established tumours, is presented. It is shown how models of this kind may be used to investigate the potential of hypothetical chemotherapy strategies, and to identify general principles for successful treatment. The model is intended to be an aid to clinicians designing new chemotherapy programmes for diseases in which progress has been disappointing.

Antineoplastic Agents↗
PubMed2000

Mathematical modeling of mortality dynamics of mammalian populations exposed to radiation.

A mathematical model is developed which describes the dynamics of radiation-induced mortality of a non-homogeneous (in radiosensitivity) mammalian population. It relates statistical biometric functions with statistical and dynamic characteristics of a critical system in organism of specimens composing this population. The model involves two types of distributions, the normal and the log-normal, of population specimens with respect to the radiosensitivity of the critical system cells. This approach suggests a new pathway in developing the methods of radiation risk assessment.

Animals↗