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At least 991 records · Page 55Linked to original sources
PubMed2000

A mathematical method for investigating dynamic behavior of an idiotype network of the immune system. The time minimum optimal control theory.

We proposed a mathematical method to investigate an integrated property of an idiotype immune network under the time minimum optimal control. The transient changes of amounts of B cell receptor bound antibodies and immune complex in the network system were expressed by detailed differential equations. The rate constant for binding the second Fab arm of antibody was set as a function of coulombic repulsive force to express the influence of redistribution of electrical charges in the ligand-receptor molecular complex. We proposed time minimum optimal control strategy as an organizing principle for rapid reactions of the immune system. Based on the rigorous mathematical foundations of the optimal control theory, we determined the differential equations for co-state variables for the state variables to compute the time minimum transient changes in the amount of the species. Biological parameters in the immune reactions were utilized from the reported experimental data. Numerical computation disclosed that influence of changes in a rate constant extended to all the species of the network. Changes in a rate constant in a different B cell system reinforced the collaborations among the idiotypes and lead them to set in motion the ejection of the antigen. Simulation of reported experimental data by the present method was successful. There were, however, some inevitable dissociations between reported experimental data and computed results. The present method will be available for evaluating the time minimum reaction of the immune network system.

Journal Article↗
PubMed2003

Mathematical modeling of drug release from bioerodible microparticles: effect of gamma-irradiation.

Bioerodible polymers used in controlled drug delivery systems, such as poly(lactic-co-glycolic acid) (PLGA) undergo radiolytic degradation during gamma-irradiation. In spite of the considerable practical importance, yet only little knowledge is available on the consequences of this sterilization method on the resulting drug release patterns in a quantitative way. The major objectives of the present study were: (i) to monitor the effects of different gamma-irradiation doses on the physicochemical properties of drug-free and drug-loaded, PLGA-based microparticles; (ii) to analyze the obtained experimental results using adequate mathematical models; (iii) to get further insight into the occurring physical and chemical phenomena; and (iv) to relate the applied gamma-irradiation dose in a quantitative way to the resulting drug release rate. 5-Fluorouracil-loaded, PLGA-based microparticles were prepared with an oil-in-water solvent extraction method and exposed to gamma-irradiation doses ranging from 0 to 33 kGy. Size exclusion chromatography, differential scanning calorimetry, scanning electron microscopy, particle size analysis, determination of the actual drug loading and in vitro drug release kinetics were used to study the effects of the gamma-irradiation dose on the physicochemical properties of the microparticles. Two mathematical models-a simplified and a more comprehensive one-were used to analyze the experimental results. The simplified model considers drug diffusion based on Fick's second law for spherical geometry and a Higuchi-like pseudo-steady-state approach. The complex model combines Monte Carlo simulations (describing polymer erosion) with partial differential equations quantifying drug diffusion with time-, position- and direction-dependent diffusivities. Interestingly, exponential relationships between the gamma-irradiation dose and the initial drug diffusivity within the microparticles could be established. Based on this knowledge both models were used to predict the resulting drug release kinetics as a function of the gamma-irradiation dose. Importantly, the theoretical predictions were confirmed by experimental results.

Dose-Response Relationship, Radiation↗
PubMed2000

Mathematical modelling of metabolism.

Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology.

Animals↗
PubMed2003

Assessing auditory nerve recovery function with a modified subtraction method: results and mathematical modeling.

OBJECTIVE: One of the main difficulties in electrical compound action potential (ECAP) recordings is to reduce the stimulus artifact due to electrical stimulation. The neural response telemetry (NRT) system of the Nucleus 24 cochlear implant extracts the ECAP response using a forward-masking (standard) subtraction technique. However, it has been shown that this subtraction technique may distort the ECAP responses in certain situations. In order to improve ECAP recordings, a modified forward-masking subtraction technique was recently proposed (Ear Hear. 21 (2000) 280). This modified subtraction technique can be applied to recovery function measurement. The objective of this study is to compare results obtained with the modified method to those obtained using the standard method. METHODS: ECAP responses were recorded in 4 adult patients using a Nucleus 24 cochlear implant. Data were collected for the 20 active electrodes. For each electrode, measurements consisted of the recovery function recording using 16 different Masker-Probe intervals. The modified method was then applied and the results compared with the standard method. RESULTS: Comparison between the two methods revealed that results were different when using the standard or modified method. Using the modified method, more ECAP responses were obtained (61.8 vs. 44.2%), but the P1 peak was sometimes attenuated; when using the standard method, N1 peak was missing in many cases. A mathematical model has been established and the mathematical simulation confirms the results obtained in patients. CONCLUSIONS: The results suggest that both methods have limitations and advantages. The modified subtraction method seems to be better for analyzing ECAP recordings in recovery function measurement because of the higher number of responses obtained compared to the standard method.

Adult↗
PubMed2003

Mathematical model for predicting biliary therapeutic endoscopic retrograde pancreatography (ERCP).

INTRODUCTION: Magnetic resonance cholangiopancreatography is as sensitive as endoscopic retrograde pancreatography in the evaluation of biliary tract diseases but does not offer therapeutic options. The aim of the present study was to develop a mathematical model to predict 'therapeutic endoscopic retrograde pancreatography' using clinical variables so that patients with low probability could be more appropriately investigated by magnetic resonance cholangiopancreatography in future. METHODS: Endoscopic retrograde pancreatography cases between January 1996 to December 1997 were retrospectively reviewed (before introduction of magnetic resonance cholangiopancreatography). Clinical, biochemical and radiological variables were analysed and a model was developed using multiple logistic regression. RESULTS: Case notes for 573 patients were successfully reviewed. A total of 330 patients underwent therapeutic endoscopic retrograde pancreatography (sphincterotomy or stent insertion). Clinical indications of obstructive jaundice and cholangitis, ultrasonographic findings of dilated common bile duct, and raised liver function tests (two or more elevated parameters) were each found to be predictive for 'therapeutic' endoscopic retrograde pancreatography. Using these variables, the mathematical model in the present study has specificity of 77% and sensitivity of 75% at the probability level of 50% or higher. This model has been tested in a separate group of endoscopic retrograde pancreatography cases carried out in 1998 and was found to have sensitivity 77.6%, specificity 80.3%, positive predictive value 68.5% and negative predictive value 86.6%. CONCLUSIONS: The model reported in the present study can help clinicians to identify cases for therapeutic endoscopic retrograde pancreatography and diagnostic magnetic resonance cholangiopancreatography.

Adolescent↗
PubMed2003

Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling.

Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorders such as osteoporosis, osteoarthritis, and Paget's disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. The model predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Paget's disease. Parametric analysis demonstrated that the mode of dynamic behavior in the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor beta. Moreover, simulations demonstrated that nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process of remodeling in normal bone and in pathological conditions such as osteoporosis and Paget's disease.

Autocrine Communication↗
PubMed2000

Mathematical modelling of the within-host dynamics of Plasmodium falciparum.

The development of malaria due to Plasmodium falciparum is a complex, multi-stage process. It is usually characterized by an exponential growth in the number of parasite-infected erythrocytes, followed by marked oscillations in this number with a period of 48 h, which are eventually dampened. This course of events has been the subject of various mathematical models. In this paper we propose a new mathematical model for the in-host asexual erythrocytic development of P. falciparum malaria. Synchronicity of the infection is shown to be an inherent feature of infection, irrespective of the duration of merozoite release from the liver. It will, therefore, cause periodic symptoms, as known in malaria patients. We also simulate the effects of an induced host immune response and show how the level of immunity affects the development of disease. The simulations fit well with the clinical observations. We show how infection can become asynchronous and discuss the effect of desynchronization on the circulating and total parasitaemia and demonstrate that synchronized broods will show parasitaemia fluctuations.

Animals↗
PubMed1992

The epidemiology of varicella-zoster virus infections: a mathematical model.

Herpes-zoster is caused by the reactivation of varicella-zoster virus (VZV). In this paper different hypotheses of how this re-emergence of virus comes about are reviewed and discussed. From these hypotheses, and epidemiological data describing the initial transmission of the virus, a mathematical model of primary disease (varicella) and reactivated disease (zoster) in developed countries is derived. The steady-state age distributions of zoster cases predicted by this model are compared with the observed distribution, derived from a review and analysis of published epidemiological data. The model allows differentiation between published hypotheses in which age of host may or may not influence the probability of viral reactivation. The results indicate that the probability of reactivation must increase with age to allow the observed pattern of zoster cases. The basic mathematical model presented provides a conceptual framework, which may be extended to assess possible control programmes.

Adolescent↗
PubMedDate not supplied

Mathematical models for the spatial receptive-field organization of nonlagged X-cells in dorsal lateral geniculate nucleus of cat.

Spatial receptive fields of relay cells in dorsal lateral geniculate nucleus (dLGN) have commonly been modeled as a difference of two Gaussian functions. We present alternative models for dLGN cells which take known physiological couplings between retina and dLGN and within dLGN into account. The models include excitatory input from a single retinal ganglion cell and feedforward inhibition via intrageniculate interneurons. Mathematical formulas describing the receptive field and response to circular spot stimuli are found both for models with a finite and an infinite number of ganglion-cell inputs to dLGN neurons. The advantage of these models compared to the common difference-of-Gaussians model is that they, in addition to providing mathematical descriptions of the receptive fields of dLGN neurons, also make explicit contributions from the geniculate circuit. Moreover, the model parameters have direct physiological relevance and can be manipulated and measured experimentally. The discrete model is applied to recently published data (Ruksenas et al., 2000) on response versus spot-diameter curves for dLGN cells and for the retinal input to the cell (S-potentials). The models are found to account well for the results for the X-cells in these experiments. Moreover, predictions from the discrete model regarding receptive-field sizes of interneurons, the amount of center-surround antagonism for interneurons compared to relay cells, and distance between neighboring retinal ganglion cells providing input to interneurons, are all compatible with data available in the literature.

Animals↗
PubMed2003

Flavor release measurement by atmospheric pressure chemical ionization ion trap mass spectrometry, construction of interface and mathematical modeling of release profiles.

An instrumental on-line retronasal flavor analysis was developed to obtain information about the release of flavor compounds in expired air from humans during eating. The volatile flavor compounds were measured by ion trap mass spectrometry with an atmospheric pressure chemical ionization source (APCI). An interface was designed to sample the breath directly from the nose. The repeatability in vitro for seven different flavor compounds came out with relative standard derivation less than 10% in most cases, which is acceptable. In vitro quantification was carried out by a determination of the concentration in the gas phase over a flavor solution by GC/MS, followed by measurements of intensities by the APCI ion trap. Ion suppression by acetone in the breath was negligible at concentration levels relevant in these experiments. The instrumental limits of detection for menthone and menthol coincide with that of the flavor detection threshold. An application study on the release of menthone and menthol from chewing gum by a group of six test persons was performed. Flavored chewing gum was used as a model matrix because of the long chewing periods and the simplicity of the system. It is concluded that the interface and the method can be used to measure breath from the nose. A mathematical model of the data was developed to give a quantitative method for description and characterization of the release of flavor compounds. The release profiles consisted of two sequences, one for a chewing period, and one for a phasing out process. The proposed method for modeling provided a reasonable description of the release process. In addition to flavor compounds, this new interface and mathematical application could provide information on chemicals in the human breath, which could be interesting, for example, within medical diagnosis.

Journal Article↗
PubMed2000

A mathematical model for kinetic study of analyte permeation from both liquid and gas phases through hollow fiber membranes into vacuum

A mathematical model and a Matlab-5 computer code have been developed to study the dynamic response of the hollow fiber membrane probe. The depletion layer formation at the sample/membrane interface is taken into consideration by the mathematical model for the liquid mobile phase. The code produces concentration profiles within a sample feed stream and in the membrane. Flux values at the vacuum side of the membrane can also be calculated as a function of time. The method can be applied both for gas and liquid feed streams. Concentration profiles in a mobile phase and the flux of analytes through the hollow fiber membrane inlet have been studied with this simulation technique as a function of the liquid-phase flow rate. The influence of the formation of a layer of the analyte depletion during the dynamic response has been considered. The shape of the depleted layer and selectivity of permeation from a liquid mobile phase through the membrane into the vacuum are shown to be dependent on the mobile-phase flow rate. In addition, for studied conditions, formation of a depletion layer is demonstrated to be fast compared with membrane diffusion. Thus, if a homogeneous aqueous sample is coming through the inlet cross-section of a hollow fiber membrane containing pure water, the response time mostly depends on analyte diffusivity in the membrane. However, if the aqueous sample is coming through the inlet cross-section of a hollow fiber membrane containing clean air, response time also depends on equilibrium analyte concentration in the depletion layer.

Journal Article↗
PubMedDate not supplied

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

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

Cell Division↗
PubMed2002

Dissolution of nonuniformly distributed immiscible liquid: intermediate-scale experiments and mathematical modeling.

The purpose of this work is to examine the effect of nonuniform distributions of immiscible organic liquid on dissolution behavior, with a specific focus on the condition dependency of dissolution (i.e., mass transfer) rate coefficients associated with applying mathematical models of differing complexities to measured data. Dissolution experiments were conducted using intermediate-scale flow cells packed with sand in which well-characterized zones of residual trichloroethene (TCE) and 1,2-dichloroethane (DCA) saturation were emplaced. A dual-energy gamma radiation system was used for in-situ measurement of NAPL saturation. Aqueous concentrations of TCE and DCA measured in the flow-cell effluent were significantly less than solubility, due primarily to dilution associated with the nonuniform immiscible-liquid distribution and bypass flow effects associated with physical heterogeneity. A quantitative analysis of flow and transport was conducted using a three-dimensional mathematical model wherein immiscible-liquid distribution, permeability variability, and sampling effects were explicitly considered. Independent values for the initial dissolution rate coefficients were obtained from dissolution experiments conducted using homogeneously packed columns. The independent predictions obtained from the model provided good representations of NAPL dissolution behavior and of total TCE/DCA mass removed, signifying model robustness. This indicates that for the complex three-dimensional model, explicit consideration of the larger scale factors that influenced immiscible-liquid dissolution in the flow cells allowed the use of a dissolution rate coefficient that represents only local-scale mass transfer processes. Conversely, the use of simpler models that did not explicitly consider the nonuniform immiscible-liquid distribution required the use of dissolution rate coefficients that are approximately 3 orders of magnitude smaller than the values obtained from the column experiments. The rate coefficients associated with the simpler models represent composite or lumped coefficients that incorporate the effects of the larger scale dissolution processes associated with the nonuniform immiscible-liquid distribution, which are not explicitly represented in the simpler models, as well as local-scale mass transfer. These results demonstrate that local-scale dissolution rate coefficients, such as those obtained from column experiments, can be used in models to successfully predict dissolution and transport of immiscible-liquid constituents at larger scales when the larger scale factors influencing dissolution behavior are explicitly accounted for in the model.

Ethylene Dichlorides↗
PubMed2003

Decontamination of polyaromatic hydrocarbons from soil by steam stripping: mathematical modeling of the mass transfer and energy requirement.

For cleaning of contaminated soil from polyaromatic hydrocarbons (PAH), a thermal separation process is applied. The process uses superheated steam that is supplied through a nozzle together with a suspension (approximately 40% soil content) of the contaminated soil into a tube reactor. In the reactor, the soil suspension is vaporized, and the PAH are stripped from the soil at temperatures of 140-300 degrees C. In a cyclone, a solid-vapor separation is carried out, and after going through a condenser, a separation of the condensed water and the PAH is obtained. For improvement of the economical performance, a heat recovery is integrated. This is realized by preheating the water/stream supplied to the evaporator by cooling the vapor steam leaving the reactor. For the mathematical description of the process, the removal of the PAH from the soil is considered to take place by a desorption process. Sorption isotherms are measured by batch experiments and can be described by isotherms of Langmuir type. A dispersion model is used to describe the mass transfer of the process. The process is mathematically modeled for instationary and stationary operation. The simulation predicts the lowest energy consumption at a good cleaning performance at a steam-to-suspension ratio of 5.

Adsorption↗
PubMed2000

A mathematical model of uterine dynamics and its application to human parturition.

We have developed a simple mathematical model with three physiologically significant states to describe the changes in intrauterine pressure associated with a contraction during human parturition. The myometrium is modelled as a set of smooth muscle cells, each of which is in one of three states (quiescent, contracted, refractory) at a given time. These states are occupied according to a cycle governed by three temporal parameters. The solutions of the equations describing the model show an oscillatory behavior for particular values of these parameters, which is very similar to the time dependent development of intrauterine pressure during labor. Due to its non-linear terms, our model could lead to chaotic oscillations (in the mathematical sense), whose clinical counterpart may occur in cases of dystocia. Despite its simplicity, this model appears to be a useful guide to further investigations of the oscillatory behavior of the myometrium, or other smooth muscles, in normal and pathological situations.

Dystocia↗
PubMed1998

Mathematical modelling as a tool to study population dynamics between sulfate reducing and methanogenic bacteria.

The existing mathematical models of sulphate fed anaerobic reactors are reviewed. Special attention was put on pecularities of the description of sulphide inhibition and competition between sulphate reduction and methanogenesis in such systems. The paper also presents an integrated mathematical model of the functioning of a sulphate fed granular sludge reactor taking into account concentration gradients on substrates, intermediates, products and bacteria inside the reactor as well as multiple-reaction stoichiometry and kinetics. The developed model includes the following blocks: a) hydrodynamic block describing liquid flow as well as transport and distribution of the components along the reactor height; b) kinetic block including growth, metabolism, inhibition and competition of acidogenic, acetogenic, methanogenic and sulphate reducing bacteria in the system; c) physico-chemical block for calculation of pH in each compartment of the liquid phase; d) transfer block describing a mass transfer of gaseous components from the liquid to the gas phase. The integrated model was calibrated and validated using laboratory studies on the functioning of sulphidogenic granular sludge reactors, i.e. their start-up and the maximization of sulphide yield in these reactors. The modelling of the reactor operation is supplemented with hypothetical computer simulations to illustrate the influence of engineering parameters on the operation performance and sulphate conversion of sulphidogenic reactors.

Algorithms↗
PubMed1990

Percutaneous absorption of benzoic acid across human skin. I. In vitro experiments and mathematical modeling.

The percutaneous absorption of benzoic acid across human skin in vitro was experimentally and mathematically modeled. Skin partition coefficients were measured over a range of benzoic acid concentrations in both saline and distilled water. The permeation of benzoic acid was measured across isolated stratum corneum, stratum corneum and epidermis, and split-thickness skin. These experiments demonstrated that the stratum corneum was the rate-limiting barrier and that the flux is proportional to the concentration of the undissociated species. The permeation data were analyzed with a comprehensive non-steady-state mathematical model of diffusion across skin. Two adjustable parameters, the effective skin thickness and diffusivity, were fit to the permeation data by nonlinear regression.

Benzoates↗
PubMed2002

Which approach to anticoagulation management is best? Illustration of an interactive mathematical model to support informed decision making.

BACKGROUND: Among patients with atrial fibrillation or mechanical heart valves, determining the best approach to oral anticoagulation largely depends on comparing the costs of anticoagulation management with the costs of events (thromboembolism and bleeding) averted. The Anticoagulation Management Event/Cost Model (ACME) is an interactive mathematical model intended to help clarify these trade-offs. METHODS: The ACME is a series of linked, nested spreadsheets. At the least detailed level, the user specifies the percentage of patients falling into various management strategies (no anticoagulation, usual physician care, anticoagulation service, patient self-testing/self-management), and the ACME estimates event rates and costs. At more detailed levels the ACME performs a series of weighted average calculations combining, for example, utilization times unit price. Cost categories are divided into event-related and management-related costs (costs of management, testing, and medication). RESULTS: Regardless of how anticoagulation is subsequently managed, perhaps the greatest benefit is obtained by moving patients who are not currently receiving anticoagulation onto warfarin. Additional benefits can be obtained by eliminating outliers (extremely high or extremely low anticoagulation levels). If changing to a more intensive approach also serves to reduce the tendency for physicians to prescribe anticoagulate below the optimal range, additional savings can be anticipated. The cost calculation typically involves a trade-off between increased up-front costs of anticoagulation management versus greater down-line savings associated with a decreased number of events. To assess the quality of anticoagulation within a given organization, it is critical to know the distribution of clotting levels for the population under anticoagulation. CONCLUSIONS: Interactive mathematical models, if sufficiently well documented, can be helpful in clarifying decisions regarding costs and benefits of various methods of anticoagulation.

Anticoagulants↗