Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “MATHEMATICS”

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 1,117 records · Page 62Linked to original sources
PubMed1994

Prediction of the comparative intensity of pneumoconiotic changes caused by chronic inhalation exposure to dusts of different cytotoxicity by means of a mathematical model.

A multicompartmental mathematical model has been used to simulate variations in the cytotoxicity of dusts in the kinetics of the retention, in the pulmonary region and tracheobronchial lymph nodes, of practically insoluble quartzite and titanium dioxide dust particles deposited on the free surfaces of the acini from alveolar air. Experiments with these dusts were conducted on rats exposed to virtually the same dust concentrations in the air for an experimental period of 20 weeks and a period of 10 weeks after exposure. Satisfactory approximation to the experimental data on the retention of these dusts is obtained by using the model parameters that depend either on damage to lung macrophages by phagocytosed particles or on the response of the host organism to this damage by enhanced recruitment of neutrophilic leucocytes; all the other variables of the model being unchanged. The values of the "action integral" computed from this model and multiplied by the index of comparative cytotoxicity of particles in vitro satisfactorily approximate to quantitative differences in the intensity of pneumoconioses caused by the dusts under study by the end of the experimental period. On the whole, the results of the mathematical model agree with the hypothesis that the cytotoxicity of particles plays a key part in both the process of retention of dust in the lung parenchyma and lung associated lymph nodes, and the pathological process caused by the retained dust. Thus given the factors and conditions on which the deposition of practically insoluble dusts in the pulmonary region depends, it is necessary to take into account the multiplicative nature of these two effects of cytotoxicity when predicting the comparative risk of pneumoconiosis.

Animals↗
PubMed2004

Investigating ethnic inequalities in the incidence of sexually transmitted infections: mathematical modelling study.

OBJECTIVES: To investigate ethnic differences in rates of gonorrhoea using empirical sexual behaviour data in a simple mathematical model. To explore the impact of different intervention strategies in this simulated population. METHODS: The findings from cross sectional studies of gonorrhoea rates and sexual behaviour in three ethnic groups in south east London were used to determine the parameters for a deterministic, mathematical model of gonorrhoea transmission dynamics, in a population stratified by sex, sexual activity (rate of partner change), and ethnic group (white, black African, and black Caribbean). We compared predicted and observed rates of infection and simulated the effects of targeted and population-wide intervention strategies. RESULTS: In model simulations the reported sexual behaviours and mixing patterns generated major differences in the rates of gonorrhoea experienced by each subpopulation. The fit of the model to observed data was sensitive to assumptions about the degree of mixing by level of sexual activity, the numbers of sexual partnerships reported by men and women, and the degree to which observed data underestimate female infection rates. Interventions to reduce duration of infection were most effective when targeted at black Caribbeans. CONCLUSIONS: Average measures of sexual behaviour in large populations are inadequate descriptors for the epidemiology of gonorrhoea. The consistency between the model results and empirical data shows that profound differences in gonorrhoea rates between ethnic groups can be explained by modest differences in a limited number of sexual behaviours and mixing patterns. Targeting effective services to particular ethnic groups can have a disproportionate influence on disease reduction in the whole community.

Adolescent↗
PubMed2002

The impact of HIV epidemic phases on the effectiveness of core group interventions: insights from mathematical models.

Mathematical models have highlighted the disproportionate contribution of core group transmitters to the spread of sexually transmitted diseases. Because the effectiveness of interventions varies with time, it has been suggested that epidemic phases should be considered in the design of prevention strategies. This study aimed to examine the impact of HIV epidemic phases on the effectiveness of HIV interventions based on gonorrhoea screening and condom use, targeted to core groups. The results are based on a mathematical model of gonorrhoea and HIV transmission in a relatively slow spreading HIV epidemic using Cotonou (Benin) as an example. For epidemics with a low reproductive potential modest core group interventions can significantly reduce HIV incidence and prevalence. As the epidemic matures, effective interventions should also incorporate core and non-core populations. For epidemics with a high reproductive potential, core group interventions are necessary but not sufficient to have a rapid and large scale impact. A more general population approach is also needed early in the epidemic. Epidemic phases are also important in the evaluation of prevention strategies.

Benin↗
PubMed1976

Death rates of bacterial spores: mathematical models.

The concave survivor curves produced as a result of spore heterogeneity were analyzed to determine whether they were caused by inmate characteristics of the spores or by the acquisition of heat resistance during the heating process. Mathematical models developed for the two hypotheses revealed that the concave survivor curve (on semi-log paper) caused by innate heterogeneity is parabolic and that caused by acquired heat resistance is exponential. The mathematical models were applied to several published survivor curves of different organisms, and heat resistance parameters and the cause of curvilinearity were determined. For the cases studied, the cause of curvilinearity appears to be acquisition of heat resistance rather than innate heterogeneity of spore population.

Adaptation, Biological↗
PubMed2006

Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes.

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate kinase I-homoserine dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves the way for a more generalized prediction of the behavior of bifunctional enzymes.

Algorithms↗
PubMed2001

Can we model nitric oxide biotransport? A survey of mathematical models for a simple diatomic molecule with surprisingly complex biological activities.

Nitric oxide (NO) is a remarkable free radical gas whose presence in biological systems and whose astonishing breadth of physiological and pathophysiological activities have only recently been recognized. Mathematical models for NO biotransport, just beginning to emerge in the literature, are examined in this review. Some puzzling and paradoxical properties of NO may be understood by modeling proposed mechanisms with known parameters. For example, it is not obvious how NO can survive strong scavenging by hemoglobin and still be a potent vasodilator. Recent models do not completely explain how tissue NO can reach effective levels in the vascular wall, and they point toward mechanisms that need further investigation. Models help to make sense of extremely low partial pressures of NO exhaled from the lung and may provide diagnostic information. The role of NO as a gaseous neurotransmitter is also being understood through modeling. Studies on the effects of NO on O2 transport and metabolism, also reviewed, suggest that previous mathematical models of transport of O2 to tissue need to be revised, taking the biological activity of NO into account.

Animals↗
PubMed2002

A mathematical model of metabolic insulin signaling pathways.

We develop a mathematical model that explicitly represents many of the known signaling components mediating translocation of the insulin-responsive glucose transporter GLUT4 to gain insight into the complexities of metabolic insulin signaling pathways. A novel mechanistic model of postreceptor events including phosphorylation of insulin receptor substrate-1, activation of phosphatidylinositol 3-kinase, and subsequent activation of downstream kinases Akt and protein kinase C-zeta is coupled with previously validated subsystem models of insulin receptor binding, receptor recycling, and GLUT4 translocation. A system of differential equations is defined by the structure of the model. Rate constants and model parameters are constrained by published experimental data. Model simulations of insulin dose-response experiments agree with published experimental data and also generate expected qualitative behaviors such as sequential signal amplification and increased sensitivity of downstream components. We examined the consequences of incorporating feedback pathways as well as representing pathological conditions, such as increased levels of protein tyrosine phosphatases, to illustrate the utility of our model for exploring molecular mechanisms. We conclude that mathematical modeling of signal transduction pathways is a useful approach for gaining insight into the complexities of metabolic insulin signaling.

Animals↗
PubMed1992

Mathematical modeling of human cardiovascular system for simulation of orthostatic response.

This paper deals with the short-term response of the human cardiovascular system to orthostatic stresses in the context of developing a mathematical model of the overall system. It discusses the physiological issues involved and how these issues have been handled in published cardiovascular models for simulation of orthostatic response. Most of the models are stimulus specific with no demonstrated capability for simulating the responses to orthostatic stimuli of different types. A comprehensive model incorporating all known phenomena related to cardiovascular regulation would greatly help to interpret the various orthostatic responses of the system in a consistent manner and to understand the interactions among its elements. This paper provides a framework for future efforts in mathematical modeling of the entire cardiovascular system.

Blood Pressure↗
PubMed1998

Estimation of nitric oxide production and reaction rates in tissue by use of a mathematical model.

Nitric oxide (NO) produced by the vascular endothelium is an important biologic messenger that regulates vessel tone and permeability and inhibits platelet adhesion and aggregation. NO exerts its control of vessel tone by interacting with guanylyl cyclase in the vascular smooth muscle to initiate a series of reactions that lead to vessel dilation. Previous efforts to investigate this interaction by mathematical modeling of NO diffusion and reaction have been hampered by the lack of information on the production and degradation rate of NO. We use a mathematical model and previously published experimental data to estimate the rate of NO production, 6.8 x 10(-14) micromol . micron-2 . s-1; the NO diffusion coefficient, 3,300 micron2 s-1; and the NO consumption rate coefficient in the vascular smooth muscle, 0.01 s-1 (1st-order rate expression) or 0.05 microM-1 . s-1 (2nd-order rate expression). The modeling approach is discussed in detail. It provides a general framework for modeling the NO produced from the endothelium and for estimating relevant physical parameters.

Endothelium, Vascular↗
PubMed1998

Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model.

The mechanisms underlying many important properties of the human atrial action potential (AP) are poorly understood. Using specific formulations of the K+, Na+, and Ca2+ currents based on data recorded from human atrial myocytes, along with representations of pump, exchange, and background currents, we developed a mathematical model of the AP. The model AP resembles APs recorded from human atrial samples and responds to rate changes, L-type Ca2+ current blockade, Na+/Ca2+ exchanger inhibition, and variations in transient outward current amplitude in a fashion similar to experimental recordings. Rate-dependent adaptation of AP duration, an important determinant of susceptibility to atrial fibrillation, was attributable to incomplete L-type Ca2+ current recovery from inactivation and incomplete delayed rectifier current deactivation at rapid rates. Experimental observations of variable AP morphology could be accounted for by changes in transient outward current density, as suggested experimentally. We conclude that this mathematical model of the human atrial AP reproduces a variety of observed AP behaviors and provides insights into the mechanisms of clinically important AP properties.

Action Potentials↗
PubMed2000

Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodeling.

Dogs have been used extensively to study atrial arrhythmias, but there are no published mathematical models of the canine atrial action potential (AP). To obtain insights into the ionic mechanisms governing canine atrial AP properties, we incorporated formulations of K(+), Na(+), Ca(2+), and Cl(-) currents, based on measurements in canine atrial myocytes, into a mathematical model of the AP. The rate-dependent behavior of model APs corresponded to experimental measurements and pointed to a central role for L-type Ca(2+) current inactivation in rate adaptation. Incorporating previously described regional ionic current variations into the model largely reproduced AP forms characteristic of the corresponding right atrial regions (appendage, pectinate muscle, crista terminalis, and atrioventricular ring). When ionic alterations induced by tachycardia-dependent remodeling were incorporated, the model reproduced qualitatively the AP features constituting the cellular substrate for atrial fibrillation. We conclude that this ionic model of the canine atrial AP agrees well with experimental measurements and gives potential insights into mechanisms underlying functionally important electrophysiological phenomena in canine atrium.

Action Potentials↗
PubMed2006

A mathematical model of twin-twin transfusion syndrome with pulsatile arterial circulations.

The twin-twin transfusion syndrome (TTTS) is a severe complication of monochorionic twin pregnancies caused by a net transfusion of blood from one twin (the donor) to the other (the recipient) through placental anastomoses. To examine the pathophysiology of TTTS evolving through clinical stages I to IV, we extended our mathematical model to include pulsating circulations propagating along the arterial tree as well as placental and cerebral vascular resistances, and arterial wall thickness and stiffness. The model demonstrates that abnormal umbilical arterial flow (TTTS stage III) in the donor twin results from increased placental resistance as well as reduced resistance in the cerebral arteries. In contrast, recipient twin abnormal umbilical arterial flow requires a significantly greater increase in placental resistance, resulting from the compressive effects of high amniotic fluid pressure. Thus simulated abnormalities of donor umbilical arterial pulsations occur in the donor more commonly and earlier than in the recipient. The "normal" staging sequence (I, II, III, IV) correlates with the presence of compensating placental anastomoses, constituting the majority of monochorionic twin placentas. However, TTTS stage III may occur before manifestations of stage II (lack of donor bladder filling), in our model correlating with severe TTTS from a single arteriovenous anastomosis, an infrequent occurring placental angioarchitecture. In conclusion, this mathematical model describes the onset and development of the four stages of TTTS, reproduces a variety of clinical manifestations, and may contribute to identifying the underlying pathophysiology of the staging sequence in TTTS.

Chorion↗
PubMed1993

A mathematical model of oscillatory insulin secretion.

Insulin is secreted in sustained oscillatory fashion from isolated islets of Langerhans. This finding has led to the assumption of an underlying synchronizing process that coordinates insulin oscillations. This assumption was tested by developing a mathematical model of oscillatory insulin secretion in which we included degree of synchrony as a parameter. We first evaluated insulin oscillations in perifused isolated rat islets, using spectral analysis to determine their regularity and frequency. A parsimonious mathematical model was developed to account for these characteristics. The model postulates a group of secretory units discharging at discrete intervals with the same underlying period. Variation from two sources, phase differences between units (synchrony) and regularity within units, is introduced by adding two normally distributed random variables with standard deviations (Sg and Si, respectively) to the secretory period. Sets of 100 simulations for different values of Sg and Si were run. Results of the simulations suggest that the system tolerates a relatively large degree of asynchrony yet still demonstrates regularity of oscillations on spectral analysis. Comparison with perifusion data suggests that a moderate degree of asynchrony between islets can best account for the pattern of insulin oscillations observed. This model provides a theoretical basis for the study of mechanisms for insulin oscillations.

Adenoma↗
PubMed1989

Determinants and limits of pressure-preset ventilation: a mathematical model of pressure control.

In recent years, four square-wave modes of pressure-preset mechanical ventilation (PPV)--pressure control, pressure support, inverse ratio, and airway pressure release ventilation--have been introduced to clinical practice. Conceptually, they share important features. Yet, because there remains widespread uncertainty regarding their ventilatory characteristics, efficacy, and appropriate use, the potential range of application is only now being investigated. To construct a unifying mathematical model of PPV, we developed a system of equations for prediction of the major "outcome" variables of PPV--tidal volume, minute ventilation, auto-positive end-expiratory pressure, mean alveolar pressure, and mechanical work--from the primary clinical "inputs" from patient (resistance, compliance) and clinician (applied pressure, frequency, inspiratory time fraction). Our analysis revealed distinct bounding limits for the outcome variables of ventilation and pressure and important implications for their clinical determinants. Although simplifying assumptions were required to enable construction of this mathematical analogue of respiratory system behavior, this model provides a firm conceptual framework for understanding the physiological interactions between PPV and the patients they are intended to help.

Humans↗
PubMed2003

VO2, VCO2, and RQ in a respiratory chamber: accurate estimation based on a new mathematical model using the Kalman-Bucy method.

A respiratory chamber is used for monitoring O(2) consumption (Vo(2)), CO(2) production (Vco(2)), and respiratory quotient (RQ) in humans, enabling long term (24-h) observation under free-living conditions. Computation of Vo(2) and Vco(2) is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. To improve the accuracy of the results, a new mathematical model is suggested in the present study explicitly accounting for the presence of such uncertainties and error sources and enabling the use of optimal filtering methods. Experiments have been realized, injecting known gas quantities and estimating them using the proposed mathematical model and the Kalman-Bucy (KB) estimation method. The estimates obtained reproduce the known production rates much better than standard methods; in particular, the mean error when fitting the known production rates is 15.6 +/- 0.9 vs. 186 +/- 36 ml/min obtained using a conventional method. Experiments with 11 humans were carried out as well, where Vo(2) and Vco(2) were estimated. The variance of the estimation errors, produced by the KB method, appears relatively small and rapidly convergent. Spectral analysis is performed to assess the residual noise content in the estimates, revealing large improvement: 2.9 +/- 0.8 vs. 3,440 +/- 824 (ml/min)(2) and 1.8 +/- 0.5 vs. 2,057 +/- 532 (ml/min)(2), respectively, for Vo(2) and Vco(2) estimates. Consequently, the accuracy of the computed RQ is also highly improved (0.3 x 10(-4) vs. 800 x 10(-4)). The presented study demonstrates the validity of the proposed model and the improvement in the results when using a KB estimation method to resolve it.

Carbon Dioxide↗
PubMed2006

Reproduction of MIGET retention and excretion data using a simple mathematical model of gas exchange in lung damage caused by oleic acid infusion.

The multiple inert-gas elimination technique (MIGET) is a complex mathematical model and experimental technique for understanding pulmonary gas exchange. Simpler mathematical models have been proposed that have a limited view compared with MIGET but may be applicable for use in clinical practice. This study examined the use of a simple model of gas exchange to describe MIGET retention and excretion data in seven pigs before and following lung damage caused by oleic acid infusion and subsequently at different levels of positive end-expiratory pressure. The simple model was found to give, on average, a good description of MIGET data, as evaluated by a chi(2) test on the weighted residual sum of squares resulting from the model fit (P > 0.2). Values of the simple model's parameters (dead-space volume, shunt, and the fraction of alveolar ventilation going to compartment 2) compared well with the similar MIGET parameters (dead-space volume, shunt, log of the standard deviation of the perfusion, log of the standard deveation of the ventilation), giving values of bias and standard deviation on the differences between dead-space volume and shunt of 0.002 +/- 0.002 liter and 7.3 +/- 2.1% (% of shunt value), respectively. Values of the fraction of alveolar ventilation going to compartment 2 correlated well with log of the standard deviation of the perfusion (r(2) = 0.86) and log of the standard deviation of the ventilation (r(2) = 0.92). These results indicate that this simple model provides a good description of lung pathology following oleic acid infusion. It remains to be seen whether physiologically valid values of the simple model parameters can be obtained from clinical experiments varying inspired oxygen fraction. If so, this may indicate a role for simple models in the clinical interpretation of gas exchange.

Animals↗
PubMed2005

A validated mathematical model of cell-mediated immune response to tumor growth.

Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations. The functions describing tumor-immune growth, response, and interaction rates, as well as associated variables, are developed using a least-squares method combined with a numerical differential equations solver. Parameter estimates and model validations use data from published mouse and human studies. Specifically, CD8+ T-tumor and NK-tumor lysis data from chromium release assays as well as in vivo tumor growth data are used. A variable sensitivity analysis is done on the model. The new functional forms developed show that there is a clear distinction between the dynamics of NK and CD8+ T cells. Simulations of tumor growth using different levels of immune stimulating ligands, effector cells, and tumor challenge are able to reproduce data from the published studies. A sensitivity analysis reveals that the variable to which the model is most sensitive is patient specific, and can be measured with a chromium release assay. The variable sensitivity analysis suggests that the model can predict which patients may positively respond to treatment. Computer simulations highlight the importance of CD8+ T-cell activation in cancer therapy.

Animals↗
PubMedDate not supplied

Nonlinear mechanics of the inner ear and its relation to otoacoustic emissions: two steps on the way to a mathematical model of DPOAE generation.

Among clinical users of the registration of distortion product otoacoustic emissions (DPOAE), the understanding of the basic causality and interpretation of the phenomenon is not yet widely spread, nor is the expected influence of the middle ear and ear canal clear. On the other side, the effort in mathematical modeling of middle and inner ear structures is driven very far by now. We are convinced, though, that the essentials of an effect as DPOAE generation must be understandable from quite simple models. In a first step de Boer's one-dimensional model was adopted and expanded by a weak frictional and a weak elastic nonlinearity, respectively. By means of perturbation theory the weakly nonlinear problem is converted in an approximation series of linear problems. So it is solvable by the common methods of linear differential equations (DEs), above all the superposition principle can be used. At the same time a structure of causality is introduced: Sources for outgoing waves are in first order approximation formed by incoming waves, and so they can be localized. The calculations show clearly that of all six cubic distortions only the 2f(1) - f(2) term does have a source in its 'allowed' region and so can travel outward. We can use the calculated DPOAE to study the influence of middle ear, external ear canal and probe plug. Some problems remain: the weakly nonlinear model in first order does not give account for proper L(dp) = f(L(1), L(2)) and L(dp) = f(f(2)/f(1)) dependency, nor does it deliver additional sources or the effect of additional suppressor tones. In a second step, therefore, we replace de Boer's simple model basilar membrane (BM) by a doubly resonant, coupled tectorial/basilar membrane (TM/BM) system. By feedback now we introduce a strong nonlinearity, which we can mathematically care for by an iterative feedback loop. The algorithm shapes the incoming waves according to strong compressive nonlinearity. More relastic incoming waves yield better source terms, and after optimization of the mistuning function between TM and BM the model now is able to deliver qualitatively correct L(dp) (L(1),L(2)) and L(dp)(f(2)/f(1)) dependencies.

Basilar Membrane↗