Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Model”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 505 records · Page 28Linked to original sources
PubMed1992

On the application of mathematical models of schistosome transmission dynamics. II. Control.

Mathematical models have considerable potential as aids to the design of schistosome control programmes. This is because of the complex nature of the schistosome transmission cycle and the variety of control measures available, which make the comparative effectiveness of different control options extremely difficult to predict. This review aims to demonstrate how control can be incorporated in models of schistosome transmission dynamics, and to make explicit the assumptions and limitations of the models and their relationships with field data. A basic model is described which considers changes in the mean number of schistosomes per person. The criteria for the eradication of endemic infection and the potential for reducing levels of infection are discussed. The treatment of various control measures within this framework is reviewed. These include: chemotherapy (mass, selective and targeted), molluscicide application (blanket and focal) and other snail control measures, larval stage control, improved water supplies and sanitation, and health education. The incorporation of economic variables is also discussed. The choice between different control options depends on the relationships between schistosome epidemiology and the costs and effects of control. The evaluation of cost-effectiveness is a dynamic problem, and the outcome will depend on local conditions and constraints. Very general recommendations for the design of schistosome control programmes are unlikely to prove useful.

Animals↗
PubMed1975

Application of a programmable pocket calculator to a single compartment mathematical model of solute kinetics.

A single compartment mathematical model has been applied to kinetics of small solutes (urea and creatinine) in dialysis therapy. The model can be described by two equations requiring iterative solution of calculated values, given several measurable variables. The equations have been programmed onto a Hewlett-Packard 65 pocket calculator and recorded on 3 X 1/2" magnetic strips, facilitating clinical application to dialysis therapy.

Computers↗
PubMed1996

A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description.

We developed and analyzed the mathematical model of the intrinsic pathway based on the current biochemical data on the kinetics of blood coagulation individual stages. The model includes eight differential equations describing the spatio-temporal dynamics of activation of factors XI, IX, X, II, I, VIII, V, and protein C. The assembly of tenase and prothrombinase complexes is considered as a function of calcium concentration. The spatial dynamics of coagulation was analyzed for the one-dimensional case. We examined the formation of active factors, their spreading, and growth of the clot from the site of injury in the direction perpendicular to the vessel wall, into the blood thickness. We assumed that the site of injury (in the model one boundary of the space segment under examination) becomes a source of the continuous influx of factor XIa. In the first part, we described the model, selected the parameters, etc. In the second part, we compared the model with experimental data obtained in the homogeneous system and analyzed the spatial dynamics of the clot growth.

Blood Coagulation↗
PubMed2001

Mathematical model of the evolution of statoconia.

A mathematical model of the evolution of statoconia in statocysts of freshwater snails based on the analysis of experimental data [Wiederhold et al., 1990; Pedrozo et al., 1996; Gao et al., 1997; Gao and Wiederhold, 1997; Wiederhold et al., 1999] is proposed. The growth of statoconia is considered as the process of solution crystallization. The model proposed assumes that two main processes determine the evolution of statoconia in developing snails: the generation of new statoconia and the linear growth of statoconia sizes. The analytical solution of the model and qualitative comparison of theoretical results with the experimental data show: (1) there are at least three periods of statoconia evolution; (2) the generation of new statoconia mainly determines the first period of evolution when the shell diameter of snails D < 4 mm; (3) when D > 6 mm the size distribution of statoconia is determined by the growth of their sizes with a constant rate; (4) on the interval deltaD = 4-6 mm the transformation of size distribution with selective dissolution of statoconia takes place. The model agrees well with the experimental data and makes it possible to estimate some parameters of the statoconia kinetics. Additional experiments, which are necessary for further development of the model, and quantitative estimates of the mechanisms of statoconia evolution are formulated.

Animals↗
PubMed2005

A mathematical model of crystallization in an emulsion.

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker-Doring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers "sucking" monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Journal Article↗
PubMed1975

Carboxyhemoglobin in nonsmokers: a mathematical model.

A study was made of existing mathematical models for both carbon monoxide (CO) and carboxyhemoglobin (COHb) buildup. From these models a combined model was derived for calculating delta%COHb in nonsmokers in an enclosed space in which excess concentrations of CO may occur. For simplicity the model was restricted to those occasions where CO concentration was at equillibrium or came to equillibrium in a time-short compared with exposure time. The equation derived was for delta%COHb calculated from CO, ventilation, respiration, persons, smokers, height, weight, cigarettes, and exposure time. Comparisons with published data show excellent agreement of calculated and observed values.

Aerospace Medicine↗
PubMed1985

Mathematical models of central pattern generators in locomotion: II. Single limb models for locomotion in the cat.

Three mathematical models of central pattern generation for locomotion in the single limb of the cat are presented. In each model, the activities in populations of neurons controlling limb joint flexors and extensors are described by a system of nonlinear differential equations. Each solution of the system for a different set of parameters corresponds to a simulation of some gait of the cat. Model I is based on unit generators for each limb joint muscle group and assumes that flexors inhibit their paired extensors, but not vice-versa. Model IIa assumes that flexors and extensors are mutually inhibitory, but that only the flexors have inherent oscillatory capability. Model IIb assumes flexors and extensors are mutually inhibitory and that both flexors and extensors have oscillatory capability. The properties of each of these models are explored, compared and contrasted, and discussed in relation to the experimental literature. All three models are shown to be capable of generating patterns consistent with various stepping rates of the cat and to show appropriate muscle sequencing and flexor-extensor interactions. Further, all three models exhibit smooth initiation and termination of stepping. However, Model I seems to provide a more parsimonious account of producing changes in stepping rate and is preferred, therefore, over models IIa and IIb.

Journal Article↗
PubMedDate not supplied

A mathematical model for irrigated epicardial radiofrequency ablation.

A mathematical model for epicardial radiofrequency ablation using an electrode irrigated by saline is proposed. Saline flow profiles are derived using thin film theory, and heat convection due to blood flow is also included in the model. Results from a computer implementation of the model using a finite element method suggest that transmural ablation lesions can be made in 4-mm-thick tissue. Effects of parameters such as tissue and saline layer thickness, irrigation rate, blood flow rate, and applied power are investigated. Saline is found to irrigate as well as ablate. Rise in saline temperature and consequent ablation by saline is more pronounced as saline layer becomes thicker. Electrode tip temperatures as much as 40 degrees C lower than maximum tissue temperature were found in simulations.

Blood Flow Velocity↗
PubMed1995

A mathematical model of radiation field edge localization.

A mathematical model of the average edge slope across the radiation field border in a portal image was investigated in order to improve the precision of edge localization in a previously reported algorithm for automatic extraction of the radiation field from double- and single-exposure portals. The model involves a global rather than a local approach to edge localization, and employs a hyperbolic function with four parameters to characterize the behavior of the radiation field penumbra. The location of the radiation field edge is determined from one of these parameters. This model was tested on a group of portal images acquired with different conditions in our clinic. Evaluation results of this model and improvements in the performance of our portal image segmentation algorithm will be presented.

Algorithms↗
PubMed1999

Five pediatric head and brain mathematical models for use in internal dosimetry.

UNLABELLED: Mathematical models of the head and brain currently used in pediatric neuroimaging dosimetry lack the anatomic detail needed to provide the necessary physical data for suborgan brain dosimetry. To overcome this limitation, the Medical Internal Radiation Dose (MIRD) Committee of the Society of Nuclear Medicine recently adopted a detailed dosimetric model of the head and brain for the adult. METHODS: New head and brain models have been developed for a newborn, 1, 5, 10 and 15 y old for use in internal dosimetry. These models are based on the MIRD adult head and brain model and on published head and brain dimensions. They contain the same eight brain subregions and the same head regions as the adult model. These new models were coupled with the Monte Carlo transport code EGS4, and absorbed fractions of energy were calculated for 14 sources of monoenergetic photons and electrons in the energy range of 10 keV-4 MeV. These absorbed fractions were then used along with radionuclide decay data to generate S values for all ages for 99mTc, considering 12 source and 15 target regions. RESULTS: Explicit transport of positrons was also considered with separation of the annihilation photons component to the absorbed fraction of energy in the calculation of S values for positron-emitting radionuclides. No statistically significant differences were found when S values were calculated for positron-emitting radionuclides under explicit consideration of the annihilation event compared with the traditional assumption of a uniform distribution of 0.511-MeV photons. CONCLUSION: The need for electron transport within the suborgan brain regions of these pediatric phantoms was reflected by the relatively fast decrease of the self-absorbed fraction within many of the brain subregions, with increasing particle energy. This series of five dosimetric head and brain models will allow more precise dosimetry of radiopharmaceuticals in pediatric nuclear medicine brain procedures.

Adult↗
PubMed2000

Mathematical models for predicting G-duration tolerances.

Mathematical models that predict fatigue-based G-duration tolerances for relaxed and straining subjects are developed and validated using published data. These models are based on regression analysis calculations using published G-duration tolerance data of relaxed subjects exposed to 3-5 G and subjects exposed to 6-9 G using an anti-G suit and performing the anti-G straining maneuver. These G-duration models are derived from published G-level tolerance models based on intravascular hydrostatic pressures and physiologic responses to maximum voluntary contractions (MVC%). Included in the validation of these models are the baroreceptor and muscle contraction cardiovascular reflexes that support arterial BP. A basic energy pool that supports a G-duration of 140 s for G exposures > 5 G is theorized. Because of the long duration of sustained G exposures in these models, the physiologic dynamics involved in predicting straining G-duration tolerances, are identified and validated using different time periods, i.e., Phases I and II. These models, based on sustained G exposures to a constant G level are also applicable to exposures of variable G levels known as simulated aerial combat maneuver (SACM) G-profile tolerances. G-duration tolerances > 9 G are predicted using these models for subjects using reclined-seat backs and positive pressure breathing.

Aerospace Medicine↗
PubMed2004

The role of mathematical modeling in evidence-based malaria control.

Mathematical models have long provided basic insights for malaria control. The recent success of the Onchocerciasis Control Program in west Africa shows that models can make great pragmatic contributions to intervention programs if the modeling is integrated into the overall program, and if the participants are clear about what models can and cannot do. This lesson can be applied to evidence-based malaria control.

Animals↗
PubMed1983

[Hyperthermia caused by ultrasonics: trials of mathematical modelling].

We describe preliminary results concerning the mathematical modelling of the hyperthermia induced by an ultrasound transducer. The developed method should allow to predict in advance the local temperatures in every clinical case, as well as to conceive and optimize more complex ultrasound generators.

Hyperthermia, Induced↗
PubMedDate not supplied

[A mathematical model of segmentation in vertebrate somitogenesis].

A mathematical model for the mechanism of periodic pattern formation in the process of somitogenesis is proposed. It is assumed that metameric arrangement first appears before somite formation at the stage of transition of mesodermal into presomitic cells. It is assumed that the transition occurs in a certain phase of the mitotic cycle and that it can be suppressed due to excretion of some transition inhibitor by presomitic cells. The model demonstrates that periodicity can appear as a result of interaction of the wave of somitogenic cell determination with the mitotic cycles of mesodermal cells. It is shown that the model naturally explains synchrony in the somite formation and the results of heat shock experiments.

Animals↗
PubMed1994

Mathematical modelling of chemotherapy in HIV infection.

A mathematical model of CD4+ lymphocyte depletion in HIV infection is used to simulate and analyse the effect of AZT treatment. In most cases, permanent administration of AZT is observed to stop the CD4+ lymphocyte count decline and to stimulate their increase up to a new steady-state level, which depends on the intensity of AZT treatment, i.e. AZT dose. Temporary administration of AZT leads only to a temporary increase in CD4+ lymphocyte count. After the treatment is terminated, the count starts to decline again. However, the resulting prolongation of patient's survival exceeds the time interval of AZT administration. Interestingly, the survival prolongation is greater, if the treatment is started at five than at two years after the infection and there is no striking increase in survival time if a dose of AZT inhibiting 75% of HIV proliferation is used instead of a lower one inducing 25% inhibition only.

CD4 Lymphocyte Count↗
PubMed1993

[Application of the mathematical model to forecast the incidence rates of seasonal infectious diseases].

The incidence rates of infectious diseases were selected and analysed according to data from the Beijing Railway Area during 1981-1991. We put forward the mathematical model to forecast the incidence rate of dysentery each quarter in 1992. The best mathematical model was selected from analysis of precision, and very useful in the prevention and treatment of seasonal infectious diseases.

China↗
PubMed2004

A mathematical model for breast cancer lesion estimation: electrical impedance technique using TS2000 commercial system.

We present a mathematical model to analyze transadmittance data for the detection of breast cancer using TransScan TS2000 commercial system. The model was constructed based on the assumption that a lesion exists near the surface of a breast region. The breast region that is considered as a background is assumed to be homogeneous at least near the surface where we attach a planar array of electrodes. Based on the model, we developed a lesion estimation algorithm utilizing single- or multifrequency transadmittance data. The approximate ratio of two conductivity values for the lesion and background needs to be known to estimate the size of the lesion even though the location estimate does not require this ratio. From the results of numerical simulations with added noise, we suggest better ways of interpreting TS2000 transadmittance images for the detection of breast cancer with improved accuracy. Since this study provides a rigorous mathematical modeling of TS2000 commercial system, it will be possible to apply the technique to lesion estimation problems based on more realistic models of breast regions in future studies.

Breast Neoplasms↗
PubMedDate not supplied

Study and mathematical modeling of the production of propionic acid by Propionibacterium acidipropionici immobilized in a stirred tank fermentor.

A mathematical model was developed that describes production of propionic acid by fermentation of sweet whey with Propionibacterium acidipropionici immobilized in calcium polygalacturonate beads in a fermentor-type stirred tank. This mathematical model is constituted by a partial differential equations system, which fits consumption, production, growth and internal diffusion rates in the support. Fermentation was experimentally studied with free cells and immobilized cells, effective diffusivities of lactose and propionic acid were estimated in the support, and typical parameters of the model were obtained by nonlinear regression of the experimental data. The variance analysis shows that the combination of micro(max) and K(d) parameters is the source of variation most significative, also they were found to be the most sensitive parameters of the model. Finally, an effectiveness factor was calculated in order to assess the effect of mass transfer on the overall reaction rate observed.

Cell Division↗