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At least 955 records · Page 53Linked to original sources
PubMed2006

A mathematical model for copper homeostasis in Enterococcus hirae.

Copper is an essential micronutrient for life. It is required by a wide range of species, from bacteria to yeast, plants and mammals including humans. To prevent the consequences of the excess or deficit of copper, living organisms have developed molecular mechanisms that regulate the uptake, efflux, storage and use of the metal. However, the limits of homeostatic regulation are not known. Here, we take advantage of a simple biological mechanism involved in copper metabolism of Enterococcus hirae, to explore how the regulation is achieved by using a set of four proteins codified in the cop operon: two P-type ATP-ases copper transporters, one copper chaper-one and one Cu-response transcription factor. We propose a mathematical model, based on differential equations and the power-law formalism (see M.A. Savageau, Chaos 11(1) (2001) 142-159), for the behavior of the cop operon and we show that homeostasis is a result of transient dynamics. The results derived from the mathematical model allow to measure qualitatively the adaptability of the system to its environment. This detailed model has been possible thanks to the available experimental biological information provided in a sequence of recent works by Solioz and co-workers.

Computer Simulation↗
PubMed2005

Mathematical modeling of Echinococcus multilocularis transmission.

A mathematical model for the transmission cycle of Echinococcus multilocularis would be useful for estimating its prevalence, and the model simulation can be instrumental in designing various control strategies. This review focuses on the epidemiological factors in the E. multilocularis transmission cycle and the recent advances of mathematical models for E. multilocularis transmission.

Animals↗
PubMedDate not supplied

Mathematical determination of external defibrillators needed at mass gatherings.

OBJECTIVE: To develop a mathematical formula that assists in determining the number of automated external defibrillators (AEDs) needed at sites of mass gatherings. METHODS: Twenty (10 male, 10 female) healthy volunteers (equally divided between age groups 21-30 and 31-40 years) responded to mock cardiac arrests in a sports stadium. Seven different first-responder scenarios were simulated (ascending and descending three separate stairway slopes (22 degrees, 39 degrees, and 69 degrees ), as well as a response across a horizontal (0 degrees ) surface. To assess the impact of spectator congestion, the same volunteers conducted each scenario in an empty and full stadium. The quantitative relationship between time and distance was then plotted for each situation. Using the quantitative relationship, the area a first responder can cover in a specified time was calculated. RESULTS: The formula for the total number of AEDs needed in a stadium (or other mass gathering site) can be expressed as follows: Total AEDs=[A(1)/(Ds(1)xDh(1))]+[A(2)/(Ds(2)xDh(2))]+[A(3)/(Ds(3)xDh(3))] where A(1), A(2), and A(3) represent the total areas of a stadium with a slight, moderate, or steep stairway slope, respectively; Ds(1), Ds(2), and Ds(3) represent the stairway distance a first responder must ascend or descend for each slope; and Dh(1), Dh(2), and Dh(3) are the horizontal distances a responder can run in the time remaining. CONCLUSION: Given a medical director's targeted response times and goals, the optimal number of AEDs required at a mass gathering can be calculated using time versus distance relationships. Future studies should evaluate the impact of the mathematically derived optimal number of AEDs at mass gatherings.

Adult↗
PubMed2005

Digital imaging analysis with mathematical morphology and fractal dimension for evaluation of periapical lesions following endodontic treatment.

OBJECTIVE: To see if a method for digitizing trabecular pattern of bone could be used to quantitatively evaluate changes in bone pattern following endodontic treatment of teeth with periapical osteolytic lesions. STUDY DESIGN: Periapical radiographs were digitized and further processed with mathematical morphology operations known as skeletonization. The trabecular patterns resulting from this skeletonization process were further analyzed with fractal dimension analysis using box-counting. RESULTS: The periapical area in digitized radiographic images showed fractal behavior. Twenty-five of 27 patients showed increase of the fractal dimension after root canal treatment. Significant changes of the box-counting could be noted 3 months after root canal treatment (P < .05). CONCLUSIONS: Mathematical morphology operation and box-counting might be helpful in early detection of changes of periapical trabecular pattern after root canal treatment.

Adult↗
PubMed2006

Mathematical modelling of the composting process: a review.

In this paper mathematical models of the composting process are examined and their performance evaluated. Mathematical models of the composting process have been derived from both energy and mass balance considerations, with solutions typically derived in time, and in some cases, spatially. Both lumped and distributed parameter models have been reported, with lumped parameter models presently predominating in the literature. Biological energy production functions within the models included first-order, Monod-type or empirical expressions, and these have predicted volatile solids degradation, oxygen consumption or carbon dioxide production, with heat generation derived using heat quotient factors. Rate coefficient correction functions for temperature, moisture, oxygen and/or free air space have been incorporated in a number of the first-order and Monod-type expressions. The most successful models in predicting temperature profiles were those which incorporated either empirical kinetic expressions for volatile solids degradation or CO2 production, or which utilised a first-order model for volatile solids degradation, with empirical corrections for temperature and moisture variations. Models incorporating Monod-type kinetic expressions were less successful. No models were able to predict maximum, average and peak temperatures to within criteria of 5, 2 and 2 degrees C, respectively, or to predict the times to reach peak temperatures to within 8 h. Limitations included the modelling of forced aeration systems only and the generation of temperature validation data for relatively short time periods in relation to those used in full-scale composting practice. Moisture and solids profiles were well predicted by two models, but oxygen and carbon dioxide profiles were generally poorly modelled. Further research to obtain more extensive substrate degradation data, develop improved first-order biological heat production models, investigate mechanistically-based moisture correction factors, explore the role of moisture tension, investigate model performance over thermophilic composting time periods, provide more information on model sensitivity and incorporate natural ventilation aeration expressions into composting process models, is suggested.

Biodegradation, Environmental↗
PubMed2000

A new mathematical neck model for a low-velocity rear-end impact dummy: evaluation of components influencing head kinematics.

A mathematical model of a new rear-end impact dummy neck was implemented using MADYMO. The main goal was to design a model with a human-like response of the first extension motion in the crash event. The new dummy neck was modelled as a series of rigid bodies (representing the seven cervical vertebrae and the uppermost thoracic element, T1) connected by pin joints, and supplemented by two muscle substitutes. The joints had non-linear stiffness characteristics and the muscle elements possessed both elastic stiffness and damping properties. The new model was compared with two neck models with the same number of vertebrae, but without muscle substitutes. The properties of the muscle substitutes and the need of these were evaluated by using three different modified neck models. The motion of T1 in the simulations was prescribed using displacement data obtained from volunteer tests. In a sensitivity analysis of the mathematical model the influence of different factors on the head-neck kinematics was evaluated. The neck model was validated against kinematics data from volunteer tests: linear displacement, angular displacement, and acceleration of the head relative to the upper torso at 7 km/h velocity change. The response of the new model was within the corridor of the volunteer tests for the main part of the time history plot. This study showed that a combination of elastic stiffness and damping in the muscle substitutes, together with a non-linear joint stiffness, resulted in a head-neck response similar to human volunteers, and superior to that of other tested neck models.

Acceleration↗
PubMed2003

The use of mathematical models to simulate control options for echinococcosis.

In many parts of the world Echinococcus granulosus is a widespread infection in sheep and dogs with a consequential spill over into the human population. In the past, mathematical models have been derived to define the transmission dynamics of this parasite, principally in the sheep-dog life cycle. These models have characterized the cycles of infection as lacking in density dependent constraints in both the definitive or intermediate hosts. This suggested that there was little, if any, induced host immunity by the parasite in either host in natural infections. However, recent evidence from both Tunisia and Kazakhstan, where young dogs are the most heavily parasitised, suggests the possibility of significant definitive host immunity. This may have an effect on the control effort needed to destabilize the parasite. A preliminary computer simulation model (based on an Excel spreadsheet) to attempt to predict the results of a control programme has been written. This demonstrates that there could be significantly different results if there is indeed protective immunity in the dog than in the absence of immunity. In the former the parasite needs a greater control effort to push the parasite towards extinction than in the latter. The computer simulation is based on a mathematical model of the parasite's life cycle and is flexible so that different values of parameters can be used in different situations where the transmission of the parasite may be at different levels. Because of the flexibility of the computer simulation it is anticipated that this programme can be applied in most situations, although initial parameters for a particular location or strain of the parasite will have to be first predetermined with base line field surveys and possibly experimental infections. The programme also has an additional flexibility to enable simulations if some parameters cannot be accurately estimated through Monte-Carlo techniques. In the latter situation, worst and best case scenarios can be estimated and likely frequency distributions of the unknown parameters can be included in the model.

Animals↗
PubMed1999

Viral kinetics and mathematical models.

Mathematical models can provide insights into the dynamics of viral diseases. Methods that were introduced to analyze human immunodeficiency virus dynamics in vivo can be modified to give insights into hepatitis C virus (HCV) dynamics, the mechanisms of action of interferon, and the consequences of giving different dosages of interferon. Patients received doses of 5, 10, or 15 mIU of interferon daily for 14 days followed by maintenance therapy of 5 mIU daily until day 90. HCV-RNA levels in serum dropped rapidly over the first 1 to 2 days of therapy. Comparing the kinetics of this response with mathematical models suggests that interferon acts by blocking the production or release of HCV virions from infected cells. The analysis further indicates that a daily dose of 5 mIU blocks approximately 80% of HCV production, and doses of 10 and 15 mIU block approximately 95% of HCV production. The serum level of HCV is approximately constant before treatment is initiated. Our model suggests that in order to maintain this constant level, on average, approximately 1 trillion virions are produced and cleared daily in an untreated HCV-infected person. The acute, rapid clearance of HCV, which occurs over the first 2 days of therapy, is followed by a slower phase of serum HCV decline. The rate of the second-phase decline may reflect the rate at which HCV-producing cells are killed, possibly by immune responses. Additional studies are needed to evaluate more fully the kinetics of the second-phase decline as well as its dose dependence and its predictive power with regard to eradication of HCV.

Antiviral Agents↗
PubMed1999

Ionic targets for drug therapy and atrial fibrillation-induced electrical remodeling: insights from a mathematical model.

UNLABELLED: Recent advances in molecular electrophysiology have made possible the development of more selective ion channel blockers for therapeutic use. However, more information is needed about the effects of blocking specific channels on repolarization in normal human atrium and in atrial cells of patients with atrial fibrillation (AF). AF-induced electrical remodeling is associated with reductions in transient outward current (Ito), ultrarapid delayed rectifier current (IKur), and L-type calcium current (ICa,L). Direct evaluation of the results of ion channel depression is limited by the nonspecificity of the available pharmacological probes. OBJECTIVES: Using a mathematical model of the human atrial action potential (AP), we aimed to: (1) evaluate the role of ionic abnormalities in producing AP changes characteristic of AF in humans and (2) explore the effects of specific channel blockade on the normal and AF-modified AP (AFAP). METHODS: We used our previously developed mathematical model of the normal human atrial AP (NAP) based on directly measured currents. We constructed a model of the AFAP by incorporating experimentally-measured reductions in Ito (50%), IKur (50%), and ICa,L (70%) current densities observed in AF. RESULTS: The AFAP exhibits the reductions in AP duration (APD) and rate-adaption typical of AF. The reduction in ICa,L alone can account for most of the morphological features of the AFAP. Inhibition of Ito by 90% leads to a reduction in APD measured at -60 mV in both the NAP and AFAP. Inhibition of the rapid component of the delayed rectifier (IKr) by 90% slows terminal repolarization of the NAP and AFAP and increases APD by 38% and 34%, respectively. Inhibition of IKur by 90% slows early repolarization and increases plateau height, activating additional IK and causing no net change in APD at 1 Hz in the NAP. In the presence of AF-induced ionic modifications, IKur inhibition increases APD by 12%. Combining IKur and IKr inhibition under both normal and AF conditions synergistically increases APD. In the NAP, altering the model parameters to reproduce other typical measured AP morphologies can significantly alter the response to K(+)-channel inhibition. CONCLUSIONS: (1) The described abnormalities in Ito, IKur and ICa,L in AF patients can account for the effects of AF on human AP properties; (2) AP prolongation by IKur block is limited by increases in plateau height that activate more IK; (3) Blockers of IKur may be more effective in prolonging APD in patients with AF; 4) Inhibition of both IKur and IKr produces supra-additive effects on APD. These observations illustrate the importance of secondary current alterations in the response of the AP to single channel blockade, and have potentially important implications for the development of improved antiarrhythmic drug therapy for AF.

Action Potentials↗
PubMed1998

Prediction by mathematical simulation of different pathophysiological effects on D-sorbitol bioavailability.

In this study a mathematical model was applied to predict how changes in hepatic extraction ratio (E), fractional portal inflow (P) and renal elimination ratio (R) may affect fractional D-sorbitol bioavailability in cirrhotic patients. D-sorbitol bioavailability was computed as the ratio between cumulative urinary outputs measured after infusion into the superior mesenteric (Uma) or the hepatic artery (Uha) and a systemic vein (Usv). The present work was aimed at explaining by mathematical simulation the very large difference observed in the regression lines when plotting Uma or Uha against Usv values. The study was performed by considering a pathophysiological model of the hepatic circulation and simulating independent variations of the above considered parameters or assuming particular pathophysiological conditions like hepatic arterialization and hepatofugal flow. Computational results account for the wide dispersion of experimental data obtained in previous studies and provide reasonable explanations of unexpected findings.

Biological Availability↗
PubMed2001

Optimization of background electrolytes for capillary electrophoresis I. Mathematical and computational model.

A mathematical and computational model is introduced for optimization of background electrolyte systems for capillary zone electrophoresis of anions. The model takes into account mono- or di- or trivalent ions and allows also for modeling of highly acidic or alkaline electrolytes, where a presence of hydrogen and hydroxide ions is significant. At maximum, the electrolyte can contain two co-anions and two counter-cations. The mathematical relations of the model are formulated to enable an easy algorithmization and programming in a computer language. The model assesses the composition of the background electrolyte in the analyte zone, which enables prediction of the parameters of the system that are experimentally available, like the transfer ratio, which is a measure of the sensitivity in the indirect photometric detection or the molar conductivity detection response, which expresses the sensitivity of the conductivity detection. Furthermore, the model also enables the evaluation of a tendency of the analyte to undergo electromigration dispersion and allows the optimization of the composition of the background electrolyte to reach a good sensitivity of detection while still having the dispersion properties in the acceptable range. Although the model presented is aimed towards the separation of anions, it can be straightforwardly rearranged to serve for simulation of electromigration of cationic analytes. The suitability of the model is checked by inspecting the behavior of a phosphate buffer for analysis of anions. It is shown that parameters of the phosphate buffer when used at neutral and alkaline pH values possess singularities that indicate a possible occurrence of system peaks. Moreover, if the mobility of any analyte of the sample is close to the mobilities of the system peaks, the indirect detector signals following the background electrolyte properties will be heavily amplified and distorted. When a specific detector sensitive on presence of the analyte were used, the signal would be almost lost due to the excessive dispersion of the peak.

Electrolytes↗
PubMed2003

Study of a mathematical model of metal ion complexes in solvent sublation.

Separation of metal ion complex, [(C(12)H(8)N(2))(3)Fe(2+)], with surfactant sodium dodecylphrate (DLS) complex from aqueous phase was carried out by solvent sublation, which obeys first-order kinetics. On the base of the complete transport mechanisms, the Langmuir adsorption, and the ion complex equilibrium in the aqueous phase, a mathematical model for the [(C(12)H(8)N(2))(3)Fe(2+)]-surfactant ion complex is obtained with the aid of the Mathematic 4.0 program, 4th Runge-Kutta method, and the Matlab programs. The effects of many parameters, such as K(a), K(l), K(ow), d(i), V(o), V(w), and Q(a), on solvent sublation are investigated. Furthermore, the simulation showed that the model is substantiated for experiments on the solvent sublation of the complex.

Journal Article↗
PubMed2000

A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis.

In this paper, a simple mathematical model developed in H.A. Levine, B.D. Sleeman, M. Nilsen-Hamilton [J. Math. Biol., in press] to describe the initiation of capillary formation in tumor angiogenesis is extended to include the roles of pericytes and macrophages in regulating angiogenesis. The model also allows for the presence of anti-angiogenic (angiostatic) factors. The model is based on the observation that angiostatin can prevent the degradation of fibronectin in the basal lamina by inhibiting the catalytic action of active proteolytic enzyme. That is, it is proposed that the inhibitor 'deactivates' the protease but that it does not reduce the over all concentration of the protease. It consequently explores the possibility of preventing neovascular capillaries from migrating through the extra-cellular matrix toward the tumor by inhibiting protease action. The model is based on the theory of reinforced random walks coupled with Michaelis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived angiogenic factors into proteolytic enzyme which in turn degrade the basal lamina. A simple catalytic reaction is proposed for the degradation of the basal lamina by the active proteases. A mechanism, in which the angiostatin acts as a protease inhibitor is discussed which has been substantiated experimentally. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase.

Angiogenesis Inducing Agents↗
PubMed2002

Mathematical modeling of myoglobin facilitated transport of oxygen in devices containing myoglobin-expressing cells.

Low pO(2) is perhaps the most significant factor in artificial pancreas failure. In these environments, not only is the beta cell production of insulin reduced, but the cell death rate is also significantly higher. Mathematical models are developed to test the feasibility of facilitated oxygen transport in enhancing O(2) flux to genetically engineered cells in a bioartificial device such as a pancreas. For this device, it is proposed that beta cells be genetically engineered to express myoglobin throughout the cell. In addition, the significance of including myoglobin throughout the alginate matrix present to provide immuno-protection for the transplanted cells is considered. The mathematical analysis predicts that myoglobin facilitated oxygen transport has the potential of increasing the oxygen concentration at the centre of a cluster of cells (islet) with an effective radius of 100 microm by 50%. These theoretical models for myoglobin facilitated oxygen transport with homogeneous Michaelis-Menten consumption also indicate that including myoglobin in the alginate gel would beneficially improve the flux of oxygen to the transplanted cells.

Alginates↗
PubMedDate not supplied

Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression.

Mathematical analysis is carried out that completely determines the global dynamics of a mathematical model for the transmission of human T-cell lymphotropic virus I (HTLV-I) infection and the development of adult T-cell leukemia (ATL). HTLV-I infection of healthy CD4(+) T cells takes place through cell-to-cell contact with infected T cells. The infected T cells can remain latent and harbor virus for several years before virus production occurs. Actively infected T cells can infect other T cells and can convert to ATL cells, whose growth is assumed to follow a classical logistic growth function. Our analysis establishes that the global dynamics of T cells are completely determined by a basic reproduction number R(0). If R(0)< or =1, infected T cells always die out. If R(0)>1, HTLV-I infection becomes chronic, and a unique endemic equilibrium is globally stable in the interior of the feasible region. We also show that the equilibrium level of ATL-cell proliferation is higher when the HTLV-I infection of T cells is chronic than when it is acute.

Adult↗
PubMed2003

Mathematical analysis of a model describing evolution of an asexual population in a changing environment.

We investigate a mathematical model for an asexual population with non-overlapping (discrete) generations, that exists in a changing environment. Sexual populations are also briefly discussed at the end of the paper. It is assumed that selection occurs on the value of a single polygenic trait, which is controlled by a finite number of loci with discrete-effect alleles. The environmental change results in a moving fitness optimum, causing the trait to be subject to a combination of stabilising and directional selection. This model is different from that investigated by Waxman and Peck [Genetics 153 (1999) 1041] where overlapping generations and continuous effect alleles were considered. In this paper, we consider non-overlapping generations and discrete effect alleles. However in [Genetics 153 (1999) 1041] and the present work, there is the same pattern of environmental change, namely a constant rate of change of the optimum. From [Genetics 153 (1999) 1041], no rigorous theoretical conclusion can be drawn about the form of the solutions as t grows large. Numerical work carried out in [Genetics 153 (1999) 1041] suggests that the solution is a lagged travelling wave solution, but no mathematical proof exists for the continuous model. Only partial results, regarding existence of travelling wave solutions and perturbed solutions, have been established (see [Nonlin. Anal. 53 (2003) 683; An integral equation describing an asexual population in a changing environment, Preprint]). For the discrete case of this paper, under the assumption that the ratio between the unit of genotypic value and the speed of environment change is a rational number, we are able to give rigorous proof of the following conclusion: the population follows the environmental change with a small lag behind, moreover, the lag is represented using a calculable quantity.

Biological Evolution↗
PubMed1998

Mathematical models of purine metabolism in man.

Experimental and clinical data on purine metabolism are collated and analyzed with three mathematical models. The first model is the result of an attempt to construct a traditional kinetic model based on Michaelis-Menten rate laws. This attempt is only partially successful, since kinetic information, while extensive, is not complete, and since qualitative information is difficult to incorporate into this type of model. The data gaps necessitate the complementation of the Michaelis-Menten model with other functional forms that can incorporate different types of data. The most convenient and established representations for this purpose are rate laws formulated as power-law functions, and these are used to construct a Complemented Michaelis-Menten (CMM) model. The other two models are pure power-law-representations, one in the form of a Generalized Mass Action (GMA) system, and the other one in the form of an S-system. The first part of the paper contains a compendium of experimental data necessary for any model of purine metabolism. This is followed by the formulation of the three models and a comparative analysis. For physiological and moderately pathological perturbations in metabolites or enzymes, the results of the three models are very similar and consistent with clinical findings. This is an encouraging result since the three models have different structures and data requirements and are based on different mathematical assumptions. Significant enzyme deficiencies are not so well modeled by the S-system model. The CMM model captures the dynamics better, but judging by comparisons with clinical observations, the best model in this case is the GMA model. The model results are discussed in some detail, along with advantages and disadvantages of each modeling strategy.

Animals↗
PubMed1999

Mathematical modelling for intra-specific brood-parasitism: coexistence between parasite and non-parasite.

In this paper, we consider an aspect of the intra-specific brood-parasitism with a mathematical modelling. As in case of moorhen Gallinula chloropus, the case dealt with in this paper in such that just a part of the whole population has the parasitising behaviour against the individuals belonging to another part of non-parasite subpopulation that does not have such behaviour. Analysing the expected fitness gain from the brood-parasitism, we consider the condition in order that parasite individuals coexist with non-parasite ones within a population. From the mathematical modelling analysis, it is shown that the stable equilibrium frequency of parasite individuals within a population, if exists, depends on the difference among individuals in terms of the individual quality reflected to the survival probability of bred offsprings.

Animals↗