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 1,603 records · Page 89Linked to original sources
PubMed1984

Mathematical modeling of the relationship of feed efficiency, days to market weight, and costs of production.

Decreased feed efficiency and increased days to market often occur together causing an increase in production costs. By mathematical modeling, the effect of decreased feed efficiency on the growth of an animal is given and the resulting formulas for increased days to market are derived. The most general model discussed incorporates the effects on days to market weight of variable feed efficiency (above or below normal for that species) and weight loss with a subsequent growth set-back. The resulting predicted increased days to market compares well with experimental data and examples using published data are discussed. This modeling allows a good estimate of the increased costs of production due to finishing unthrifty animals, which takes into account all the variable daily costs, not just the increased total feed consumption during the period of growth to market weight.

Animal Feed↗
PubMed1988

Correction of cellular autofluorescence in flow cytometry by mathematical modeling of cellular fluorescence.

A method for the correction of background fluorescence in flow cytometry with special relevance to the quantitation of low levels of cellular surface membrane antigens is presented. The method is based on the mathematical modeling of cellular fluorescence distributions of background fluorescence (autofluorescence control or irrelevant antibody control) and total fluorescence (positively stained cells). Algorithms based on two models and utilizing only the routinely available background and total fluorescence histograms are developed and implemented in computer programs. These allow estimation of the fluorescence histogram corresponding exclusively to immunofluorescence staining of the cell surface antigen of interest. Thus, the correction of background fluorescence is effected solely with software processing of routinely available data; no additional hardware or parameter determinations are necessary. Two models were chosen to be physically plausible and to represent extremes in correlation between background and probe fluorescence. Extremes were chosen to assess the solution dependence on model and to provide bounds to the actual solution when no information on correlation is available. Results are presented for both computer simulations and for an actual assay of the CR1 complement receptor on human erythrocytes to test and illustrate the technique. Alternatively, data can be tested assuming a particular model to explore the relationship, if any, between specific and nonspecific fluorescence.

Algorithms↗
PubMedDate not supplied

A mathematical model for laser in situ keratomileusis and photorefractive keratectomy.

PURPOSE: The purpose of ablation refractive surgery is to remove the refractive error from the inherently asymmetric aspheric cornea. Although the technique is gaining wide acceptance and popularity, some patients are left with irregular corneas. Our objective was to develop a methodology to analyze corneal shape, reduce the shape to arcs, modify the local arc value to the desired new arc value, and render a new continuous Euclidean surface without discontinuity. METHODS: The method to reconstruct the corneal surface consists of importing scanner output elevation data points into a computer-aided design (CAD) application to form the surface model. The corneal arc measurements are derived at 5 degrees increments and centered about the Gauss point of symmetry. Each arc is manipulated to adjust the corresponding arc on the proposed corneal surface to reflect the new arc value, correcting for the refractive error. The method determines the amount of corneal tilt and ablation depth at a given diameter required for the refractive error with a smooth transition zone to the base cornea. RESULTS: The case example is a patient who began with a spherical refraction of -8.75 D and after LASIK was emmetropic, but had irregular astigmatism and 20/30 best spectacle-corrected Snellen visual acuity. The proposed mathematical model compares the achieved surface shape to the mathematically planned surface contour. An enhancement procedure to remove the LASIK-induced corneal irregularity was designed. CONCLUSION: A mathematical technique to plan myopic ablative surgery to make the corneal surface regular and symmetric is proposed.

Adult↗
PubMed1998

Parametric analysis of the relationship between end-capillary and mean tissue PO2 as predicted by a mathematical model.

An increase of the partial pressure of oxygen in venules towards larger vessels has been observed experimentally, but the mechanism of this phenomenon has not been established. The present study considers a simple mathematical model of oxygen transport from a capillary to the surrounding tissue cylinder and analyses the conditions under which the end-capillary partial pressure of oxygen is lower than the mean tissue pressure. Under these conditions oxygen would diffuse into the venules since they are surrounded by the tissue with a higher partial pressure of oxygen. Cerebral circulation is chosen for these calculations and conditions of normoxia, hypoxic hypoxia, carbon monoxide hypoxia, anemia, and polycythemia are simulated. The tissue metabolic rate is also varied. It is found that under most conditions the relationship between the end-capillary and mean tissue partial pressures of oxygen can be reversed when one of the parameters is varied within its physiological range, i.e. the difference between these variables could be either positive or negative depending on the value of the parameters. Therefore, under many realistic conditions this mechanism would contribute to an increase of the partial pressure of oxygen in the venules. This conclusion should hold for a more realistic geometrical model of capillary network, but the relationships between the end-capillary and mean tissue partial pressures of oxygen, in addition to their dependence on the parameters considered in this study, would likely be dependent on the spatial location within the network.

Animals↗
PubMed2002

Mathematical modelling of host-parasitoid systems: effects of chemically mediated parasitoid foraging strategies on within- and between-generation spatio-temporal dynamics.

In this paper we develop a novel discrete, individual-based mathematical model to investigate the effect of parasitoid foraging strategies on the spatial and temporal dynamics of host-parasitoid systems. The model is used to compare naïve or random search strategies with search strategies that depend on experience and sensitivity to semiochemicals in the environment. It focuses on simple mechanistic interactions between individual hosts, parasitoids, and an underlying field of a volatile semiochemical (emitted by the hosts during feeding) which acts as a chemoattractant for the parasitoids. The model addresses movement at different spatial scales, where scale of movement also depends on the internal state of an individual. Individual interactions between hosts and parasitoids are modelled at a discrete (micro-scale) level using probabilistic rules. The resulting within-generation dynamics produced by these interactions are then used to generate the population levels for successive generations. The model simulations examine the effect of various key parameters of the model on (i) the spatio-temporal patterns of hosts and parasitoids within generations; (ii) the population levels of the hosts and parasitoids between generations. Key results of the model simulations show that the following model parameters have an important effect on either the development of patchiness within generations or the stability/instability of the population levels between generations: (i) the rate of diffusion of the kairomones; (ii) the specific search strategy adopted by the parasitoids; (iii) the rate of host increase between successive generations. Finally, evolutionary aspects concerning competition between several parasitoid subpopulations adopting different search strategies are also examined.

Animals↗
PubMed2005

Ecological mechanisms that promote arbovirus survival: a mathematical model of Ross River virus transmission.

Many assessments of host and vector competence for arboviruses focus on level and length of infectivity and ignore ecological mechanisms that contribute to virus survival. In this paper, mathematical models are used to compare local survival mechanisms for a range of scenarios, using Ross River virus as a case study. Ross River virus is an Australian arbovirus with many mosquito vectors and reservoir hosts. The mechanisms for maintaining long-term transmission of the virus vary between salt and freshwater mosquito vectors, and according to the availability of susceptible hosts. The models demonstrate that overwintering of virus in adult freshwater mosquitoes requires a large host population, while overwintering of virus in infected eggs of saltwater mosquitoes is an effective survival strategy when filial infection rates are high. The virus survives longer when both salt and freshwater mosquito species are included in the model than when only one mosquito species is present. When the marsupial host is replaced by a host with higher birth rate and shorter infectious period, the virus survived longer under all models. This suggests that birth rate can be a key factor when assessing the competence of reservoir hosts to maintain virus transmission.

Aedes↗
PubMed1998

Fatal falls from a height: the use of mathematical models to estimate the height of fall from the injuries sustained.

The authors undertook a review of fatal falls from a height, that occurred in 1991-92 in Singapore, with the objective of constructing mathematical models relating the height of fall to the injuries sustained. The 603 cases studied showed a mean age of 41.4 years with a male to female ratio of approximately 2:1. A sub-sample of 416 (69%) of these subjects had fallen from known heights (mean, 26.9 m; range, 3-69.6 m) and were studied in further detail. Bivariate analysis of this group showed that their injury severity score (ISS) was significantly correlated with the height of fall (H) and age (P < 0.01; r = 0.412 and 0.187, respectively). As the ISS is not strictly a continuous variable and varied markedly with H, it was categorised into bands (ISSB) before being subjected to further analysis. Regression modelling to adjust for mutual confounding showed that both height of fall and age were significant independent determinants of the ISSB (P < 0.0001). A model with H as the dependent variable was then constructed to relate the height of fall to ISSB and other statistically significant indicators of the extent and the severity of the injuries sustained. A second model with bands of height (HB) as the dependent variable was similarly constructed to assess the effect of banding both height and ISS. Our findings suggested that the height of fall was significantly associated with age, ISS and the extent of injury (mostly AIS > or = 3), and confirmed the usefulness of these models for investigative purposes. Statistical models could be designed and used to assess any apparent discrepancy between injury severity as determined at autopsy and the suspected/alleged height of fall.

Accidental Falls↗
PubMed1971

A mathematical model of common-cold epidemics on Tristan da Cunha.

Records of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

Atlantic Islands↗
PubMed1994

A mathematical model of pathogenesis in idiopathic parkinsonism.

We used our observations relating clinical deficits in idiopathic parkinsonism (IP) to age and to disease duration (Lee et al, Brain 1994; 117: 501-7), to develop a mathematical model of the temporal profile of neurodegeneration in IP. We also examined other sets of relevant published observations and applied three additional assumptions which permitted the formulation of this model. Our model indicates that accelerating or decelerating processes should be excluded as the driving forces behind neuronal death in IP. Mechanisms in accord with the model include: (i) an event that kills some neurons and damages others in such a way that their life expectation is reduced; or (ii) an event that starts a process which is continuously killing healthy neurons at a constant rate. The model enables us to extrapolate back to estimate when the causal event occurred. It also explains why IP proceeds more rapidly in older patients. The model has potential relevance to other neurodegenerative disorders, such as Alzheimer's disease and amyotrophic lateral sclerosis.

Adult↗
PubMed2004

A mathematical model of the population dynamics of Heterakis gallinarum in turkeys (Meleagridis gallopavo).

Heterakis gallinarum is a relatively nonpathogenic organism, but it is important as the transport host for the pathogenic protozoan Histomonas meleagridis. A mathematical model was developed to describe the population dynamics of Heterakis gallinarum in a turkey flock to study its kinetics in a number of hosts. The model includes quantitative (parasite burden) and qualitative (number of hosts without mature parasite) descriptions of these dynamics. To understand the role of Heterakis as a transport host, the various elements that delay the beginning of development of the parasite population (e.g., necessary delay of larval stage, the probability of having a male and female in the same host) were taken into account. From published data, the negative binomial distribution parameter k = 0.24, which described the aggregated distribution of the Heterakis among the hosts, was calculated. The sensibility study showed that when the k parameter decreased (i.e., when the population was more aggregated), infestation increased quantitatively (mean parasite burden increased) but not qualitatively (the number of host without mature parasite increased). The model demonstrated that the population dynamics of Heterakis takes time; for instance, with an aggregated population of Heterakis at d 90, the host is mainly free of adult parasite. These results may be used in the future to test the role of Heterakis in the spread of Histomonas.

Animals↗
PubMed1992

Mathematical modeling of oxygen diffusion and respiration in legume root nodules.

The O(2) permeability of legume root nodules is under physiological control; decreases in permeability are triggered by various forms of stress. Two linked mathematical models were used to explore several hypotheses concerning the physical nature of the variable diffusion barrier in nodules. Respiration and diffusion of dissolved O(2) and oxygenated leghemoglobin were simulated for the nodule cortex and the nodule interior. Measured nodule permeabilities were shown to be inconsistent with the hypothesis that large numbers of air-filled pores penetrate the diffusion barrier. Changes in the affinity of leghemoglobin for O(2) or in the rate of cytoplasmic streaming in diffusion barrier cells did not result in the large changes in O(2) permeability reported for real nodules. The presence or absence, but not the thickness, of aqueous plugs in radial pores through the cortex was found to have a large effect on permeability. Flooding of intercellular spaces, either between layers of cells in the cortex or in the nodule interior, also caused large changes in simulated permeability. The unsteady-state O(2) method for determining nodule permeability was tested using data generated by the model. The accuracy of the method was confirmed, provided that certain assumptions (full oxygenation of leghemoglobin under pure O(2) and uniform conditions in the nodule interior) are met.

Journal Article↗
PubMed1991

[Statistical value of the various mathematical models in rhinomanometry].

By means of rhinomanometry, analogue physiological transnasal pressure and corresponding flow signals are simultaneously recorded during quiet nasal breathing. In order to describe the sigmoid shaped pressure/flow curves or relationship, several mathematical models have been developed. In this study, the authors wanted to demonstrate which model best describes the curvilinearity of the pressure/flow curves. By their approach, they found that polynomial models like delta p = K0 + K1V + K2V2 as well as the Broms' polar coordinate model best fit the recorded pressure/flow data. Since the parameters and exponents of such a model characterize the degree of laminar and turbulent behaviour of transnasal flow, a diagnostic potential may be offered in the future, to qualify and quantify the phenomenon of nasal obstruction.

Humans↗
PubMedDate not supplied

[Mathematical model of technical equipment of a clinical-diagnostic laboratory].

The paper is concerned with the problems of technical equipment of standard clinico-diagnostic laboratories (CDL) in this country. The authors suggest a mathematic model that may minimize expenditures for laboratory studies. The model enables the following problems to be solved: to issue scientifically-based recommendations for technical equipment of CDL; to validate the medico-technical requirements for newly devised items; to select the optimum types of uniform items; to define optimal technical decisions at the stage of the design; to determine the lab assistant's labour productivity and the cost of some investigations; to compute the medical laboratory engineering requirement for treatment and prophylactic institutions of this country.

Biochemistry↗
PubMed1982

Analysis of the ICP pulse-pressure relationship as a function of arterial blood pressure. Clinical validation of a mathematical model.

The influence of arterial blood pressure (ABP) on the intracranial pulse pressure relationship (PPR) was studied in 17 patients in 29 recordings, with a total period of registration of 71.5 hours. The relationship between ICP and ABP was analysed by sampling the data every 15 seconds during spontaneous fluctuations of both these variables, and the analysis was performed on the basis of a mathematical model which includes pulsatory components. MABP and ABP amplitude had an opposite effect on the slope of PPR. Flattening of the PPR slope was caused by a MABP increase or an ABP amplitude decrease. The slope became steeper with decreasing MABP or increasing ABP amplitude. In accordance with the theoretical assumptions the quotient MABP/ABP-AMP was found to be suitable to express these opposite effects on PPR. Qualitatively, the same pattern of reaction was found in all patients. Rapid changes in PPR occurring during monitoring can be explained by a change in MABP/ABP-AMP relationship, regardless whether ABP changes influence intracranial elastance or not. The breakpoint of the PPR was recorded only on two occasions and could be explained in one by the influence of ABP. Monitoring of PPR as a measure of intracranial elastance and correlation of PPR with the patient's condition it not permitted unless at least the influence of ABP is analysed in each individual case.

Adult↗
PubMed2002

Practical experience in the use of mathematical models to predict migration of additives from food-contact polymers.

To reduce the amount of compliance-specific migration testing for food-contact polymers, the use of migration modelling has been evaluated. The paper describes experimental work carried out on a range of plastics and compares measured migrations against predictions obtained using mathematical models. A large number of experimental migration data have been obtained and used to evaluate a Fickian-based migration model in the prediction of specific migration of additives into olive oil. All tests were conducted using olive oil, representing the most severe case for fatty foods with test conditions including 2h at 121 degrees C, 6h at 70 degrees C, 2h at 70 degrees C, 2h at 60 degrees C and 10 days at 40 degrees C, representing short-term exposures at high temperatures and room temperature storage. Predicted migrations were calculated by inputting the measured initial concentration of additive in the polymers (Cp,0) into the equations together with known variables such as additive molecular weight, temperature and exposure time. The results indicate the Piringer migration model, using the 'exact' calculations of the Migratest Lite program, predicted migrations into olive oil that were close to or in excess of the experimental results and gave an overestimation for > 95% of the migrations generated here.

Food Contamination↗
PubMed1988

Mathematical modelling of intra- and extracellular potentials generated by active structures with short regions of increased diameter.

The Hodgkin-Huxley (1952) model was used to calculate intracellular potentials by the method of Joyner et al. (1978). Extracellular potentials were estimated on the basis of a mathematical model proposed by us. It has shown that, irrespective of practical isopotentiality of the membrane of a local inhomogeneity, the latter affects extracellular potentials in two ways: 1) through changes in the potential profile in the region of the structure before the inhomogeneity; 2) through its own potential profile. The first effect is considerably greater than the second one, but the second is greater than the effect of the equal portion of the thin fibre. Increase in the diameter or length of an inhomogeneity is combined with such changes in the potential profile, that the effect of the inhomogeneity on the extracellular potential amplitude is practically independent of its actual size. The extracellular potential waveform substantially depends on the ratio of the diameters of the two parts of the structure and on the position of the inhomogeneity in relation to the sealed structure end. Registration of the positive-negative potentials having a large positive phase should not be considered as an indication of passive properties of the structure.

Extracellular Space↗