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PubMedDate not supplied

Auditory brainstem response (ABR) latency: relative importance of age, sex and sensorineural hearing-loss using a mathematical model of the audiogram.

Influences of age, sex and audiogram on ABR latencies have been studied. Using a mathematical model of audiogram, the analysis of data finds a relative importance of age, sex and audiogram similar to previous studies. Audiogram slope was correlated only with the latencies of waves I and V, and multiple regression analyses indicate the slope effect is relatively weak compared to that of the other parameters. Using a mathematical model of audiogram did not improve the ABR variance across subjects, underscoring the need to discover other relevant variables to explain ABR latency.

Acoustic Stimulation↗
PubMed2001

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions.

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Animals↗
PubMedDate not supplied

[Mathematical model of the dual action of G protein on the Ca2+ current in identified neurons of the snail Helix aspersa].

INTRODUCTION: The effect of the dopamine on the calcium current of identified cells of the snail Helix aspersa consists on an initial decrease, followed by a subsequent increase when the drug is removed. It had been previously demonstrated that this effect is mediated by a G protein, supposing that the decrease of the current would be mediated by the G alpha subunit, while the increase would be produced by the G beta gamma subunit. OBJECTIVE: A mathematical model has been developed with the object to test if the hypothesis of the dual action of the G protein could explain the experimental results. MATERIAL AND METHODS: It has been recording by means of the 'patch-clamp' (whole cell) in identified cells of snail. On the other hand, it has been developed a mathematical model of the calcium current using a Hodgkin-Huxley model, and a simulation of the action of the G protein on this current. RESULTS: Adjusting the kinetic parameters of the channel by means of the experimental data, it has reproduced in a faithful way the behavior of the calcium current. The simulation of the action of dopamine reproduces the decrease and increase of the current by means of the serial action of the G protein's subunits. CONCLUSION: Although a mathematical model cannot demonstrate the logic necessity of the hypotheses on that is based, it is unequivocally demonstrated that the hypothesis is fully compatible with experimental results.

Animals↗
PubMed2006

Mathematical modelling and numerical simulation of the morphological development of neurons.

BACKGROUND: The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other. METHODS: A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described. RESULTS: Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development. CONCLUSION: A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.

Animals↗
PubMed2006

A mathematical model for predicting the outcome in moderate head injury.

BACKGROUND: Virtually all the literature on head injury has focused on the outcome prediction of severe and mild head injuries and very few studies have been dedicated to patients sustaining moderate head injuries. AIM: To identify the patient following moderate head injury who may die, develop severe disability or significant cognitive and behavioral problems on the first day of injury itself. SETTING: Tertiary teaching hospital. DESIGN: Prospective study divided into two groups. MATERIALS AND METHODS: The study included 85 patients whose Glasgow coma scale score were 9-12 and who had isolated moderate head injury. Among the above patients a preliminary prospective study was conducted in first group of 64 patients using 7 clinical factors, 18 neuro-behavioral sequel and CT brain data in prediction of outcome with moderate head injury. From the results obtained in the above study three statistically significant factors were identified and a mathematical model was developed and used prospectively in the next 21 patients and its accuracy was evaluated. STATISTICAL METHODS USED: Multiple regression analysis and Kendall's tau non- parametric test using statistical package for social sciences (SPSS 11-5-version) were used to find out the predictive factors. RESULTS: Results of these patients showed combination of CT scan brain data, verbal response and neurological signs could provide a reliable prediction in moderate head injury. CONCLUSION: Based upon the above results a mathematical model was developed giving a value for the above-mentioned factors. The mathematical model was "CT brain data x (Verbal response + Neurological Signs)". Its overall accuracy when used on the day of admission was around 80%.

Craniocerebral Trauma↗
PubMed1995

Mathematical modeling of dendritic growth in vitro.

The dendritic branching pattern of cultured hippocampal neurons was analyzed to obtain mathematical parameters that fit the time-dependent growth of dendrites under limited extrinsic influence. Cultured neurons were stained with a non-toxic carbocyanine dye (diO) and pyramidal-shaped neurons that were physically separated from one another were analyzed at post-plating days 1, 2, 3, 4, 6 and 7. The geometric branching pattern of the dendrites was analyzed using a mathematical model that incorporates random effects in the form of a Galton-Watson branching process where splitting of one branch is statistically independent of the splitting of all other branches, and deterministic effects in the form of a parameter that measures the extent to which dense patterns (clusters) or sparse patterns (elongated trees) are formed. The geometric branching pattern of the dendrites was analyzed using a mathematical model that incorporates random and deterministic effects. The model parameters were estimated via the method of maximum likelihood. The data suggest that in vitro basal dendrites grow according to a purely random branching process without pronounced dense or sparse patterns, while apical dendrites tend to form elongated trees with fewer secondary bifurcations. This trend is quantified, and it depends on the culture conditions in which the neurons are grown. The quantitative assessment of various influences on dendritic growth patterns are discussed.

Animals↗
PubMed1989

Mathematical models of tumor growth. IV. Effects of a necrotic core.

Two mathematical models for the control of the growth of a tumor by diffusion of mitotic inhibitor are presented. The inhibitor production rate is taken to be uniform in a necrotic core for the first model and in the nonnecrotic region for the second model. Regions of stable and unstable growth are determined, and conclusions are drawn about the limiting peripheral widths of stable tissue growth for both models. Comparisons of the results from the two models indicate that the models are sensitive to the source distributions of inhibitor production.

Diffusion↗
PubMed1990

[An analysis of the effect of measles vaccination program by a mathematical model].

The reported case rates of measles during 1967-1986 were analyzed and compared with rates predicted by a mathematical model for measles prevalence. In Japan, measles vaccination was introduced in October, 1978. Since data before and after the introduction were available, the effect of the vaccination program could be analyzed. The mathematical model was constructed by modifying the Kermack-McKendrick model. In the model, environmental virus density was involved as an additional variable and the 'death' (inactivation) rate of the virus was assumed to show seasonal variation. The strategy for prevention and eradication was also discussed. The main results were as follows: 1. The characteristics of measles prevalence were (1) seasonal (annual) variation which has a peak in May or June and a bottom in September or October, (2) bienniality (before the vaccination), i.e., higher prevalence and lower prevalence years alternate every other year, and (3) trienniality (after the vaccination), i.e., a higher prevalence year appears every three years. 2. The model could reproduce all these characteristics for a range of probable parameters. 3. According to the model, trienniality was a transient phase and the system finally reached a stationary state that showed neither bienniality nor trienniality. 4. The critical density of the susceptible population necessary for the survivability of the virus in the population, was also obtainable from the model.

Computer Simulation↗
PubMed2001

Understanding the spread of antibiotic resistant pathogens in hospitals: mathematical models as tools for control.

As microorganisms become more resistant to antimicrobial agents, effective infection control measures will become increasingly important. However, despite multiple studies on infection prevention, few data exist on the quantitative effects of the individual aspects of infection control strategies. The combination of epidemiologic surveillance, molecular genotyping, observational studies on compliance, and mathematical modeling may improve our ability to determine the quantitative effects of individual infection control measures. This may help to design more effective infection control programs. In this study, we review several of the models that have been published and speculate on the usefulness of mathematical modeling for improving the prevention of infection.

Anti-Bacterial Agents↗
PubMed1988

Antigenic relationships between avian paramyxoviruses. III. A mathematical model of antigenic drift and a computer-assisted approach for construction of a phylogenetic tree.

The suggested model of antigenic kinship between related paramyxoviruses is based on another concept of antigenic determinant, as compared to the previously suggested combinatorial mathematical model by the authors. According to it, antigenic changes of any determinant do not proceed by "leaps" but can be changed gradually. Such changed determinant can induce a correspondingly changed type of antibodies which still preserve a certain kinship to the original type of the determinant (before its changing) revealed by cross reaction serological tests. Accordingly, there can be "families" of the determinants differing by degree of relatedness to (or, reversely, by antigenic distance from) the "original" ("ancestor") determinant. In addition to another interpretation of the antigenic kinship, the new mathematical model was used as an approach for revealing phylogenetic relationships between antigenically related viruses.

Antigens, Viral↗
PubMed1991

Regional myocardial stress distribution from magnetic resonance image-based mathematical models.

The instantaneous regional stress distribution within the myocardium, which cannot be directly measured, has been estimated using improved numerical methods and nonaxisymmetric biventricular geometry. To do this, we have employed computer-aided solid mathematical modeling to generate a three-dimensional representation for an ex vivo canine biventricular unit using magnetic resonance imaging. A two-dimensional transverse section was isolated from the solid mathematical model for regional stress analysis using p-version finite element analysis. Loading conditions and material property descriptions were taken from published reports. Analyses showed the maximum principal stresses to range from -1.76 X 10(5) to 8.52 X 10(5) dynes/cm2 during systolic loading, and from -3.85 X 10(4) to 1.13 X 10(5) dynes/cm2 during diastolic loading. This study demonstrates that magnetic resonance image-based solid mathematical biventricular models are suitable for regional stress analysis using p-version finite element analysis. p-Version finite element analysis using magnetic resonance image-based cardiac representations facilitates in vivo stress-strain analyses and may allow the clinical estimation of regional myocardial stress.

Animals↗
PubMed2002

Optimal range for parvalbumin as relaxing agent in adult cardiac myocytes: gene transfer and mathematical modeling.

Parvalbumin (PV) has recently been shown to increase the relaxation rate when expressed in intact isolated cardiac myocytes via adenovirus gene transfer. We report here a combined experimental and mathematical modeling approach to determine the dose-response and the sarcomere length (SL) shortening-frequency relationship of PV in adult rat cardiac myocytes in primary culture. The dose-response was obtained experimentally by observing the PV-transduced myocytes at different time points after gene transfer. Calcium transients and unloaded mechanical contractions were measured. The results were as follows. At low estimated [PV] (approximately 0.01 mM), contractile parameters were unchanged; at intermediate [PV], relaxation rate of the mechanical contraction and the decay rate of the calcium transient increased with little effects on amplitude; and at high [PV] (approximately 0.1 mM), relaxation rate was further increased, but the amplitudes of the mechanical contraction and the calcium transient were diminished when compared with control myocytes. The SL shortening-frequency relationship exhibited a biphasic response to increasing stimulus frequency in controls (decrease in amplitude and re-lengthening time from 0.2 to 1.0 Hz followed by an increase in these parameters from 2.0 to 4.0 Hz). The effect of PV was to flatten this frequency response. This flattening effect was partly explained by a reduction in the variation in fractional binding of PV to calcium during beats at high frequency. In conclusion, experimental results and mathematical modeling indicate that there is an optimal PV range for which relaxation rate is increased with little effect on contractile amplitude and that PV effectiveness decreases as the stimulus frequency increases.

Animals↗
PubMed2005

A predictive mathematical model for the calculation of the final mass of Graves' disease thyroids treated with 131I.

Substantial reductions in thyroid volume (up to 70-80%) after radioiodine therapy of Graves' hyperthyroidism are common and have been reported in the literature. A relationship between thyroid volume reduction and outcome of 131I therapy of Graves' disease has been reported by some authors. This important result could be used to decide individually the optimal radioiodine activity A0 (MBq) to administer to the patient, but a predictive model relating the change in gland volume to A0 is required. Recently, a mathematical model of thyroid mass reduction during the clearance phase (30-35 days) after 131I administration to patients with Graves' disease has been published and used as the basis for prescribing the therapeutic thyroid absorbed dose. It is well known that the thyroid volume reduction goes on until 1 year after therapy. In this paper, a mathematical model to predict the final mass of Graves' diseased thyroids submitted to 131I therapy is presented. This model represents a tentative explanation of what occurs macroscopically after the end of the clearance phase of radioiodine in the gland (the so-called second-order effects). It is shown that the final thyroid mass depends on its basal mass, on the radiation dose absorbed by the gland and on a constant value alpha typical of thyroid tissue. Alpha has been evaluated based on a set of measurements made in 15 reference patients affected by Graves' disease and submitted to 131I therapy. A predictive equation for the calculation of the final mass of thyroid is presented. It is based on macroscopic parameters measurable after a diagnostic 131I capsule administration (0.37-1.85 MBq), before giving the therapy. The final mass calculated using this equation is compared to the final mass of thyroid measured 1 year after therapy administration in 22 Graves' diseased patients. The final masses calculated and measured 1 year after therapy are in fairly good agreement (R = 0.81). The possibility, for the physician, to decide a therapeutic activity based on the desired decrease of thyroid mass instead of on a fixed thyroid absorbed dose could be a new opportunity to cure Graves' disease.

Computer Simulation↗
PubMed2004

A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice.

OBJECTIVE: To develop a simple, physiologically based mathematical model of pancreatic duct cell secretion using experimentally derived parameters that generates pancreatic fluid bicarbonate concentrations of >140 mM after CFTR activation. METHODS: A new mathematical model was developed simulating a duct cell within a proximal pancreatic duct and included a sodium-2-bicarbonate cotransporter (NBC) and sodium-potassium pump (NaK pump) on a chloride-impermeable basolateral membrane, CFTR on the luminal membrane with 0.2 to 1 bicarbonate to chloride permeability ratio. Chloride-bicarbonate antiporters (Cl/HCO3 AP) were added or subtracted from the basolateral (APb) and luminal (APl) membranes. The model was integrated over time using XPPAUT. RESULTS: This model predicts robust, NaK pump-dependent bicarbonate secretion with opening of the CFTR, generates and maintains pancreatic fluid secretion with bicarbonate concentrations >140 mM, and returns to basal levels with CFTR closure. Limiting CFTR permeability to bicarbonate, as seen in some CFTR mutations, markedly inhibited pancreatic bicarbonate and fluid secretion. CONCLUSIONS: A simple CFTR-dependent duct cell model can explain active, high-volume, high-concentration bicarbonate secretion in pancreatic juice that reproduces the experimental findings. This model may also provide insight into why CFTR mutations that predominantly affect bicarbonate permeability predispose to pancreatic dysfunction in humans.

Animals↗
PubMed1993

A mathematical model for the force and energetics in competitive running.

A simple mathematical model for competitive running is developed. This model contains the force and energy reserves as key variables and it described their relationship and dynamics. It is made up of three submodels for the biomechanics of running the energetics and the optimization. The model for the energetics is an extension of the hydraulic model of Margaria and Morton. The key geometric parameters of this piecewise linear, three compartment model are determined on the basis of well known physiological facts and data.

Adenosine Triphosphate↗
PubMed2006

A mathematical model to predict the size of the pellets formed in freeze pelletization techniques: parameters affecting pellet size.

A mathematical model was developed based on the theory of drop formation to predict the size of the pellets formed in the freeze pelletization process. Further the model was validated by studying the effect of various parameters on the pellet size such as viscosity of the pellet forming and column liquids, surface/interfacial tension, density difference between pellet forming and column liquids; size, shape, and material of construction of the needle tips and temperatures maintained in the columns. In this study, pellets were prepared from different matrices including polyethylene glycols and waxes. The column liquids studied were silicone oils and aqueous glycerol solutions. The surface/interfacial tension, density difference between pellet forming and column liquids and needle tip size were found to be the most important factors affecting pellet size. The viscosity of the column liquid was not found to significantly affect the size of the pellets. The size of the pellets was also not affected by the pellet forming liquids of low viscosities. An increase in the initial column temperature slightly decreased the pellet size. The mathematical model developed was found to successfully predict the size of the pellets with an average error of 3.32% for different matrices that were studied.

Diglycerides↗
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↗
PubMed2003

The glycolytic phenotype in carcinogenesis and tumor invasion: insights through mathematical models.

Malignant cells characteristically exhibit altered metabolic patterns when compared with normal mammalian cells with increased reliance on anaerobic metabolism of glucose to lactic acid even in the presence of abundant oxygen. The inefficiency of the anaerobic pathway is compensated by increased glucose flux, a phenomenon first noted by Otto Warburg approximately 80 years ago and currently exploited for 2-fluoro-2-deoxy-D-glucose-positron emission tomography imaging in clinical radiology. The latter has demonstrated the glycolytic phenotype is a near-universal phenomenon in human cancers. The potential role of the glycolytic phenotype in facilitating tumor invasion has been investigated through mathematical models of the tumor-host interface. Modified cellular automaton and diffusion reaction models demonstrate protons will diffuse from the tumor into peritumoral normal tissue subjecting nontransformed cells adjacent to the tumor edge to an extracellular pH significantly lower than normal. This leads to normal cell death via p53-dependent apoptosis pathways, as well as degradation of the interstitial matrix, loss of intercellular gap junctions, enhanced angiogenesis, and inhibition of the host immune response to tumor antigens. Transformed cells maintain their proliferative capacity in acidic extracellular pH because of mutations in p53 or some other component in the apoptosis pathways. This allows tumor cells to remain proliferative and migrate into the peritumoral normal tissue producing the invasive phenotype. Mathematical models of invasive cancer based on tumor-induced acidification are consistent with extant data on tumor microenvironment and results from clinical positron emission tomography imaging, including the observed correlation between tumor invasiveness and glucose utilization. Novel treatment approaches focused on perturbation of the tumor microenvironment are predicted from the mathematical models and are supported by recent clinical data demonstrating the benefits of azotemia and metabolic acidosis in survival of patients with metastatic renal cancer. The evolutionary basis for adoption of the glycolytic phenotype during carcinogenesis remains unclear because it appears to confer significant competitive disadvantages on the tumor cells due to of inefficient energy production and expenditure of resources to remove the acid byproducts. We propose that the glycolytic phenotype represents a successful adaptation to environmental selection parameters because it confers the ability to invade. That is, the glycolytic phenotype allows the cell to move from the microenvironment of a premalignant lesion to adjacent normal tissue. There it competes with normal cells that are less fit than the populations within the tumor in a microenvironment of relative substrate abundance. The consequent unrestrained proliferation allows the glycolytic phenotype to emerge simultaneous with the transition from a premalignant lesion to an invasive cancer.

Animals↗