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PubMed2006

Quantitative risk analysis of particulate matter in the air: interspecies extrapolation with bioassay and mathematical models.

We analyzed the health risk of particulate matters in the air to humans using bioassay data and a mathematical model. We designed an original dosimetry model to estimate the particle concentration in human respiratory organs, and the concentration of the inhaled particles at the target organ was used for interspecies extrapolation from rat to human. Our model is based on the conventional dosimetry model and deposition model in the previous literature, but clearance parameters have been newly introduced for the simulation of long-term exposure. Lung cancer was set as the risk endpoint in our risk study, and the dose-response relationship at the target organ (lung) was quantitatively analyzed by the benchmark dose (BMD) method. For interspecies extrapolation based on target organ concentration, we assumed benchmark concentration (BMC) related to 1% excess cancer in rats and humans, and the human equivalent concentration (HEC) was searched by back-estimation using our model. The obtained HEC was 948 to 1098 mg/m3, and the unit risk to humans was 9.11 to 10.5 x 10(-9) per 1 microg/m3 of particulate matter. The estimated cancer risk for Japanese people in general was estimated as approximately 9-10 persons per 100,000,000 when the particle concentration in the air is 10 microg/m3.

Air Pollutants↗
PubMed2006

Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development.

This paper presents a mathematical model of normal and abnormal tissue growth. The modelling focuses on the potential role that stress responsiveness may play in causing proliferative disorders which are at the basis of the development of avascular tumours. In particular, we study how an incorrect sensing of its compression state by a cell population can represent a clonal advantage and can generate hyperplasia and tumour growth with well-known characteristics such as compression of the tissue, structural changes in the extracellular matrix, change in the percentage of cell type (normal or abnormal), extracellular matrix and extracellular liquid. A spatially independent description of the phenomenon is given initially by a system of non-linear ordinary differential equations which is explicitly solved in some cases of biological interest showing a first phase in which some abnormal cells simply replace the normal ones, a second phase in which the hyper-proliferation of the abnormal cells causes a progressive compression within the tissue itself and a third phase in which the tissue reaches a compressed state, which presses on the surrounding environment. A travelling wave analysis is also performed which gives an estimate of the velocity of the growing mass.

Cadherins↗
PubMed2004

Evaluation of the influence of aircraft shielding on the aircrew exposure through an aircraft mathematical model.

In order to investigate the influence of aircraft shielding on the galactic component of cosmic rays, an aircraft mathematical model has been developed by the combinatorial geometry package of the Monte-Carlo transport code FLUKA. The isotropic irradiation of the aircraft in the cosmic ray environment has been simulated. Effective dose and ambient dose equivalent rates have been determined inside the aircraft at several locations along the fuselage, at a typical civil aviation altitude (10 580 m), for vertical cut-off rigidity of 0.4 GV (poles) and 17.6 GV (equator) and deceleration potential of 465 MV. The values of both quantities were generally lower than those in the free atmosphere. They depend, in an intricate manner, on the location within the aircraft, quantity of fuel, number of passengers, etc. The position onboard of crew members should be taken into account when assessing individual doses. Likewise due consideration must be taken when positioning detectors which are used to measure H*(10). Care would be needed to avoid ambiguity when comparing the results of calculation with the experimental data.

Aircraft↗
PubMed1997

Parameter sensitivity of a mathematical model of the anterior cruciate ligament.

This paper presents the results of an investigation into parameter sensitivity of a mathematical model of the human anterior cruciate ligament (ACL). The model ACL comprised a continuous array of fibres mapped between part-elliptical attachment areas on the femur and tibia. Relative motion of the two bones was controlled by a planar four-bar linkage. Parameter modifications were: (a) an alternative set of values for the coordinates of the four-bar linkage joints; (b) rotation of the attachment areas of the ligament by +/- 30 degrees; and (c) variation of some mechanical properties. The alternative four-bar linkage parameter set produced extremely large changes in ACL force values, up to 130 per cent. Rotating the tibial attachment changed forces by less than 20 per cent, whereas rotating the femoral attachment changed forces by up to 100 per cent. Altering the mechanical parameters produced the smallest differences in force, under 15 per cent. These results highlight the importance, when using a theoretical model, of establishing the values of the parameters defining the model as accurately as possible and of carrying out a parameter sensitivity study. From a clinical viewpoint, they also suggest that, when reconstructing a ruptured ACL, one of the most important considerations must be to position the femoral attachment of the graft as accurately as is feasible.

Anterior Cruciate Ligament↗
PubMed2002

A generalized mathematical model of biological oscillators.

Biological rhythms such as circadian rhythms, biochemical rhythms and neural oscillators are based on the mathematical model of the theory of harmonic oscillators. These are solutions of certain second-order differential equations. They can also be viewed as spherical harmonics on the circle in the two-dimensional Euclidean space. The spherical harmonics on (n-1)-spheres and, more generally, the Stiefel harmonics can represent oscillatory phenomena, and we expect that they can serve as models for more complex biological rhythms.

Algorithms↗
PubMedDate not supplied

[Mathematical model of trans-sarcomere exchange of calcium ions and Ca2+-dependent control of smooth muscle contractile activity].

The mathematical model of smooth muscles contractile activity Ca(2+)-dependent control has been proposed on the base of Ca ions trans-sarcomal exchange biochemical mechanisms interpretation in myocytes. While analysing the model the conclusion should be made that kinetic parameters changes (in relation to Ca ions) Mg2+, ATP-dependent calcium pump of plasma membrane--Michaelis constant Km and transport process maximal velocity Vmax-render the effect on the character of the intracellular calcium transients and profile of full mechanokinetic curve. As well one more conclusion has been made that plasma membrane Mg2+, ATP-dependent calcium pump, which kinetic parameters under the physiologic conditions are subjected to modulation as the result of metabolic, pharmacologic and physico-chemical factors fulfills the essential role in supplying Ca(2+)-dependent control of the smooth muscles contractile response full cycle.

Adenosine Triphosphate↗
PubMedDate not supplied

[The mathematical modeling of the optimal dose fields in radiation therapy of malignant tumors. Part 1 (Distance radiotherapy)].

The specificity of mathematical modeling of optimal dose fields in radiation therapy of malignant tumors is under consideration. The permissible dose field is set now for irradiated body as a system of linear limitations to the doses at control spots (CS) distributed in the lesion focus and in the healthy organs and tissues. It is for the first time that an issue related with choosing an adequate number and method of CS distribution, based on uniform continuity of the dose field, is addressed in the paper. An iterative procedure of building the local CS networks is suggested. The method of linear programming (LP) can be used to select an optimal irradiation plan. A method of serial input of limitations, which cuts both the LP task scope and its computer-aided solution, is described.

Algorithms↗
PubMed1987

Mathematical modelling of intra- and extracellular potentials generated by active structures: effects of a step change in structure diameter.

A mathematical model developed in our laboratory is used to estimate and analyse extracellular potentials generated in a volume conductor by a geometrically inhomogeneous structure with a step increase or a step decrease in its diameter. The transmembrane potentials were calculated using the model of Hodgkin and Huxley (1952) and the method of Joyner et al. (1978). Variations in waveforms of the transmembrane and extracellular potentials were described and discussed. Differences in waveforms of the extracellular potentials and in declines of their components are due to changes in the source which generates these potentials. In case of a propagation block the peak-to-peak amplitude of the extracellular potentials calculated over the area of the block may be higher than that over the area of propagation of action potentials. The possible applications of the results to the analysis of extracellular potentials recorded around actual motoneurons during their orthodromic or antidromic activation are discussed.

Action Potentials↗
PubMed1979

A mathematical model of the human body in health, disease, and during treatment.

This paper presents a preliminary description of a mathematical model of the human body and some details of the computer software and hardware used to study the model. The model includes many organ systems of the body and the interplay among systems. In addition to this physiological framework, a variety of diseases and therapeutic measures can be simulated. The model can be used in two different ways. In one mode, hypothetical experiments can be conducted that focus on the underlying physiological mechanisms and the complex interaction among organ systems that are essential to the maintenance of life. In a second mode, clinical encounters can be simulated in which hypothetical patients are seen, diagnosed and treated.

Acid-Base Equilibrium↗
PubMed2000

A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in china.

BACKGROUND: Before universal infant immunization against hepatitis B virus (HBV) in 1986 China was a region endemic for HBV infection. The prevalence of HBV infection in the population was about 60% and the proportion of chronic HBV carriers around 10%. These HBV carriers could progress to chronic hepatitis B, cirrhosis, and primary hepatocellular carcinoma. Since 1976, large-scale sero-surveys of HBV infection have been carried out and a lot of data have been collected. METHOD: This paper describes a mathematical model developed to predict the dynamics of HBV transmission and to evaluate the long-term effectiveness of the vaccination programme. We used a compartment model expressed by a set of partial differential equations based on the characteristics of HBV infection. RESULTS: All parameters, expressed in the model as a non-linear function of age and time since vaccination, were estimated using sero-survey data. The model fits well with both pre-vaccination and post-vaccination sero-surveys. The observed and estimated age-specific prevalence rates of HBV infection and HBV carriage agree with each other. According to our model, if all newborns are vaccinated according to schedule, the rate of HBV carriage will decline sharply over time to 0.2% in 70 years. By then, the ratio of acute hepatitis B will be less than 0.5% and the ratio of chronic hepatitis B will be around 5%. CONCLUSIONS: The results suggest that HBV infection in China can be controlled in just one generation, and eventually eliminated. Our model shows that vaccination coverage is the most important indicator for the elimination of HBV transmission. The higher the vaccination coverage, the better the long-term effectiveness of immunization. Thus, the key to controlling and eliminating HBV transmission in China is to find ways to immunize all infants throughout the country, especially in poor, rural areas.

Adolescent↗
PubMed2000

Development of a mathematical model that predicts optimal muscle activation patterns by using brief trains.

Because muscles must be repetitively activated during functional electrical stimulation, it is desirable to identify the stimulation pattern that produces the most force. Previous experimental work has shown that the optimal pattern contains an initial high-frequency burst of pulses (i.e., an initial doublet or triplet) followed by a low, constant-frequency portion. Pattern optimization is particularly challenging, because a muscle's contractile characteristics and, therefore, the optimal pattern change under different physiological conditions and are different for each person. This work describes the continued development and testing of a mathematical model that predicts isometric forces from fresh and fatigued muscles in response to brief trains of electrical pulses. By use of this model and an optimization algorithm, stimulation patterns that produced maximum forces from each subject were identified.

Algorithms↗
PubMed1991

Mathematical model for the effects of adhesion and mechanics on cell migration speed.

Migration of mammalian blood and tissue cells over adhesive surfaces is apparently mediated by specific reversible reactions between cell membrane adhesion receptors and complementary ligands attached to the substratum. Although in a number of systems these receptors and ligand molecules have been isolated and identified, a theory capable of predicting the effects of their properties on cell migration behavior currently does not exist. We present a simple mathematical model for elucidating the dependence of cell speed on adhesion-receptor/ligand binding and cell mechanical properties. Our model can be applied to propose answers to questions such as: does an optimal adhesiveness exist for cell movement? How might changes in receptor and ligand density and/or affinity affect the rate of migration? Can cell rheological properties influence movement speed? This model incorporates cytoskeletal force generation, cell polarization, and dynamic adhesion as requirements for persistent cell movement. A critical feature is the proposed existence of an asymmetry in some cell adhesion-receptor property, correlated with cell polarity. We consider two major alternative mechanisms underlying this asymmetry: (a) a spatial distribution of adhesion-receptor number due to polarized endocytic trafficking and (b) a spatial variation in adhesion-receptor/ligand bond strength. Applying a viscoelastic-solid model for cell mechanics allows us to represent one-dimensional locomotion with a system of differential equations describing cell deformation and displacement along with adhesion-receptor dynamics. In this paper, we solve these equations under the simplifying assumption that receptor dynamics are at a quasi-steady state relative to cell locomotion. Thus, our results are strictly valid for sufficiently slow cell movement, as typically observed for tissue cells such as fibroblasts. Numerical examples relevant to experimental systems are provided. Our results predict how cell speed might vary with intracellular contractile force, cell rheology, receptor/ligand kinetics, and receptor/ligand number densities. A biphasic dependence is shown to be possible with respect to some of the system parameters, with position of the maxima essentially governed by a balance between transmitted contractile force and adhesiveness. We demonstrate that predictions for the two alternative asymmetry mechanisms can be distinguished and could be experimentally tested using cell populations possessing different adhesion-receptor numbers.

Animals↗
PubMed2002

New mathematical model for accurate description of absorption kinetics of paracetamol given orally with a high calorie liquid meal.

OBJECTIVE: Gastric emptying (GE) of liquids is quantified as the rate of paracetamol absorption in clinical and research settings (paracetamol method). A conventional 1-compartment model assumes the first-order rate kinetics for paracetamol absorption. This assumption seems improper when paracetamol is coingested with a caloric liquid meal, because the caloric liquid leaves the stomach at a constant rate (zero-order process). Theories based on the 1-compartment model reveal that tmax and Cmax/AUCinfinity accurately reflect the rate of paracetamol absorption, but whether this is also the case when paracetamol is administered with a caloric liquid, has not been investigated. The aims of this study were to propose a new mathematical model for accurately describing absorptive behaviors of paracetamol added to a caloric liquid meal, and, using the model, to clarify the characteristics of tmax and Cmax/AUCinfinity as rate parameters. METHODS: Based on the newly developed model, tamx and Cmax/AUCinfinity were mathematically expressed in terms of GE rates. Subsequently, the characteristics of tmax and Cmax/AUCinfinity were elucidated by simulation works. RESULTS: The simulation study showed that both tamx and Cmax/AUCinfinity could reflect GE rates, tmax was a more sensitive index of GE than Cmax/AUCinfinity and tmax was less reliable than Cmax/AUCinfinity if GE is very rapid. CONCLUSIONS: In the paracetamol method using a caloric liquid test meal, tmax and Cmax/AUCinfinity are suitable for detecting delayed and rapid GE, respectively.

Absorption↗
PubMed2006

Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models.

BACKGROUND: Oncolytic viruses that specifically target tumor cells are promising anti-cancer therapeutic agents. The interaction between an oncolytic virus and tumor cells is amenable to mathematical modeling using adaptations of techniques employed previously for modeling other types of virus-cell interaction. RESULTS: A complete parametric analysis of dynamic regimes of a conceptual model of anti-tumor virus therapy is presented. The role and limitations of mass-action kinetics are discussed. A functional response, which is a function of the ratio of uninfected to infected tumor cells, is proposed to describe the spread of the virus infection in the tumor. One of the main mathematical features of ratio-dependent models is that the origin is a complicated equilibrium point whose characteristics determine the main properties of the model. It is shown that, in a certain area of parameter values, the trajectories of the model form a family of homoclinics to the origin (so-called elliptic sector). Biologically, this means that both infected and uninfected tumor cells can be eliminated with time, and complete recovery is possible as a result of the virus therapy within the framework of deterministic models. CONCLUSION: Our model, in contrast to the previously published models of oncolytic virus-tumor interaction, exhibits all possible outcomes of oncolytic virus infection, i.e., no effect on the tumor, stabilization or reduction of the tumor load, and complete elimination of the tumor. The parameter values that result in tumor elimination, which is, obviously, the desired outcome, are compatible with some of the available experimental data. REVIEWERS: This article was reviewed by Mikhail Blagosklonny, David Krakauer, Erik Van Nimwegen, and Ned Wingreen. OPEN PEER REVIEW: Reviewed by Mikhail Blagosklonny, David Krakauer, Erik Van Nimwegen, and Ned Wingreen. For the full reviews, please go to the Reviewers' comments section.

Journal Article↗
PubMed2000

Mathematical Modeling of Drug Release from Microemulsions: Theory in Comparison with Experiments.

The topic of this paper is the study of the drug release from a drug-loaded microemulsion by reverting to a new mathematical model overcoming some drawbacks of previously proposed models. In particular, attention is focused on the mathematical expression of the drug fluxes existing between the oil and water phases during drug release. Indeed, not only the drug release kinetics, but also the drug oil-water partition coefficient strongly depend on these fluxes. Two microemulsion are considered: the first is composed by water, Tween80 as surfactant, and Triacetin as oil phase, while the second is composed by water, Tween80 as surfactant, and a Triacetin-benzylic alcohol mixture (1 : 1) as oil phase. Both of them are loaded by Nimesulide, an oil-soluble drug of considerable industrial relevance. The drug release is performed by resorting to a permeation experiment (Franz cells apparatus) as it demonstrated to be the most reliable methodology. The good agreement between the experimental permeation data and the model best-fitting ensures that the most important phenomena ruling this kind of drug release were properly accounted for by the new proposed model. Copyright 2000 Academic Press.

Journal Article↗
PubMed1995

A mathematical model of agonist-induced propagation of calcium waves in astrocytes.

In astrocytes, calcium signals evoked by neurotransmitters appear as waves within single cells, which spread to other cells in the network. Recent analysis has shown that waves are initiated at a single invariant site in the cell and propagated within the cell in a nonlinear and saltatory manner by regenerative amplification at specific predestined cellular sites. In order to gain insight into local cellular waves and wave collisions we have developed a mathematical model of cellular wave amplification loci. This model is in good agreement with experimental data which includes: ambient calcium gradients in resting cells, wave origination and local amplification and generation of local waves. As observed in experiments, the model also predicts that different locations in the cell can have different frequencies of oscillation. The amplification loci are thought to be specialized areas of the endoplasmic reticulum membrane containing a higher density or higher sensitivity of IP3 receptors. Our analysis suggests that the cellular loci act as weakly coupled oscillators each with its intrinsic latency and frequency of oscillation. Thus the appearance of the propagated calcium wave may be a reflection of these differences rather than an actual diffusional wave propagation.

Animals↗
PubMed1987

Development of mathematical models for an in vitro-phagocytosis test system.

Phagocytosis tests have been carried out by many authors using different methods under different conditions. The results have been interpreted in different ways, as well sometimes with conflicting notations. In order to get to a more systematic data analysis and to separate intrinsic from methodic influences, the possibility to apply mathematical models to a phagocytosis test has been studied. In agreement with previous experiences that phagocytosis can well be represented by a mathematical treatment as Michaelis-Menten-type enzyme kinetics concerning its initial rate and by an exponential function under in vivo conditions, in vitro-phagocytosis was phenomenologically described as an analogon of an irreversible bimolecular chemical reaction. In this way, rate and capacity of phagocytosis may be quantified separately. On the basis of systematic deviations of the data from this model, modifications have been developed which could be connected with pertinent observations. The design of further experiments from preliminary results on the basis of our models is discussed.

Granulocytes↗
PubMed2004

Mathematical model of Listeria monocytogenes cross-contamination in a fish processing plant.

Listeriosis is a foodborne disease caused by the bacterium Listeria monocytogenes. The food industry and government agencies devote considerable resources to reducing contamination of ready-to-eat foods with L. monocytogenes. Because inactivation treatments can effectively eliminate L. monocytogenes present on raw materials, postprocessing cross-contamination from the processing plant environment appears to be responsible for most L. monocytogenes food contamination events. An improved understanding of cross-contamination pathways is critical to preventing L. monocytogenes contamination. Therefore, a plant-specific mathematical model of L. monocytogenes cross-contamination was developed, which described the transmission of L. monocytogenes contamination among food, food contact surfaces, employees' gloves, and the environment. A smoked fish processing plant was used as a model system. The model estimated that 10.7% (5th and 95th percentile, 0.05% and 22.3%, respectively) of food products in a lot are likely to be contaminated with L. monocytogenes. Sensitivity analysis identified the most significant input parameters as the frequency with which employees' gloves contact food and food contact surfaces, and the frequency of changing gloves. Scenario analysis indicated that the greatest reduction of the within-lot prevalence of contaminated food products can be achieved if the raw material entering the plant is free of contamination. Zero contamination of food products in a lot was possible but rare. This model could be used in a risk assessment to quantify the potential public health benefits of in-plant control strategies to reduce cross-contamination.

Animals↗