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At least 1,117 records · Page 62Linked to original sources
PubMed1998

Mathematical model for controlled diffusional release of dispersed solute drugs from monolithic implants.

New mathematical models are formulated and analytical solutions are presented for the diffusional release of a solute from both non-erodible and biodegradable multi-layered slab matrices in which the initial drug loading c0 is greater than the solubility limit cs. A Stefan problem with moving boundaries results from this formulation. An inward moving diffusional front separates the reservoir (unextracted region) containing the undissolved drug from the partially extracted region. The cumulative mass released is determined as a function of time. The ultimate goal of such an investigation is to provide a reliable design tool for the fabrication of specialized implantable capsule/drug combinations to deliver prespecified and reproducible dosages over a wide spectrum of conditions and required durations of therapeutic treatment. Such a mathematical/computational tool may also prove effective in the prediction of suitable dosages for other drugs of differing chemical or molecular properties without additional elaborate animal testing.

Diffusion↗
PubMed1998

A mathematical model of the inner medullary collecting duct of the rat: acid/base transport.

A mathematical model of the inner medullary collecting duct (IMCD) of the rat has been developed that is suitable for simulating luminal buffer titration and ammonia secretion by this nephron segment. Luminal proton secretion has been assigned to an H-K-ATPase, which has been represented by adapting the kinetic model of the gastric enzyme by Brzezinski et al. (P. Brzezinski, B. G. Malmstrom, P. Lorentzon, and B. Wallmark. Biochim. Biophys. Acta 942: 215-219, 1988). In shifting to a 2 H+:1 ATP stoichiometry, the model enzyme can acidify the tubule lumen approximately 3 pH units below that of the cytosol, when luminal K+ is in abundance. Peritubular base exit is a combination of ammonia recycling and HCO3- flux (either via Cl-/HCO3- exchange or via a Cl- channel). Ammonia recycling involves NH4(+) uptake on the Na-K-ATPase followed by diffusive NH3 exit [S. M. Wall. Am. J. Physiol. 270 (Renal Physiol. 39): F432-F439, 1996]; model calculations suggest that this is the principal mode of base exit. By virtue of this mechanism, the model also suggests that realistic elevations in peritubular K+ concentration will compromise IMCD acid secretion. Although ammonia recycling is insensitive to carbonic anhydrase (CA) inhibition, the base exit linked to HCO3- flux provides a CA-sensitive component to acid secretion. In model simulations, it is observed that increased luminal NaCl entry increases ammonia cycling but decreases peritubular Cl-/HCO3- exchange (due to increased cell Cl-). This parallel system of peritubular base exit stabilizes acid secretion in the face of variable Na+ reabsorption.

Animals↗
PubMed1992

A mathematical model of the human circadian system and its application to jet lag.

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid trans-meridian travel.

Body Temperature↗
PubMed1999

[Analysis of mathematical model parameters for continuous rotary annular chromatography].

The curves of analysis solution of mathematical model for continuous rotary annular chromatography (CAC) coincide with experimental results well, but some points are derived from theoretical values due to the errors from experimental method. The width and the angles of maximum mass concentration solution at outlet (retention number), except for the other experimental conditions, depend on phase equilibrium coefficient and transfer functions. Because the precision of model parameters is strongly affected by the correction of experimental method, the sensitivities of phase equilibrium coefficients and transfer functions have been studied, in which the phase equilibrium coefficient is the key parameters to improve the separation effect of CAC process.

Biotechnology↗
PubMed2003

A mathematical model for evaluating the impact of vaccination schedules: application to Neisseria meningitidis.

A mathematical model is described which determines the impact of a schedule of vaccination on the time course of a certain class of diseases. The data are the demographic variables and parameters and age-dependent non-fatal and fatal case rates. Given the age- and time-dependent rates of vaccination including coverage and corresponding efficacies, various schedules may be distinguished by either the absolute numbers of cases and deaths avoided or the numbers of cases and deaths avoided per dose of vaccine. The model was applied to meningo-coccal serogroup C disease in France. The outcomes of six different vaccination schedules were examined. In absolute terms, a schedule in which all individuals aged between 2 and 20 years were vaccinated performed best, but this schedule and that in which only 1-year olds were vaccinated performed equally and best in terms of cases prevented, but not lives saved, per dose.

Adolescent↗
PubMedDate not supplied

[Mathematical modeling of electron and protein transport, coupled with ATP synthesis in chloroplasts].

A mathematical model of electron and proton transport in chloroplasts of higher plants was developed, which takes into account the lateral heterogeneity of the lamellar system. Based on the results of numerical experiments, lateral profiles of pH in the thylakoid lumen and in the narrow gap between grana thylakoids under different metabolic conditions (in the state of photosynthetic control and under photophosphorylation conditions) were simulated. Lateral profiles of pH in the thylakoid lumen and in the intrathylakoid gap were simulated for different values of the proton diffusion coefficient and stroma pH. The model demonstrated that there might be two mechanisms of regulation of electron and proton transport in chloroplasts: (1) the slowing down of noncyclic electron transport due to a decrease in the intrathylakoid pH, and (2) the retardation of plastoquinone reduction due to slow diffusion of protons inside the narrow gap between the thylakoids of grana.

Adenosine Triphosphate↗
PubMed2006

[Mathematical modeling of laser-induced selective destruction of labyrinthine vestibular receptors].

Basing on mathematical modeling, we tried to investigate in humans the ability of laser energy to suppress the function of the ampullar receptors of the semicircular canels and otolith receptors; to elicit mechanism of action of laser energy on labyrinthine receptors. Modeling has shown that in 1 mm thickness of the canal wall laser impact raises temperature of the liquid to 120 degrees C. Temperature higher than 100 degrees C stands in it up to 120 ms. This induces a distinct hydrodynamic shock which suppresses function of labyrinthine ampullar and otolith receptors. The heat factor of the laser impact causes destruction of the receptor sensory cells lasting for about a year.

Ear Diseases↗
PubMedDate not supplied

[Mathematical model of movement of asymmetrical erythrocyte along the capillary].

The proposed 3-dimensional mathematical model describes the motion of asymmetrical erythrocytes through capillaries of different sections. The lubrication theory is used to describe the flow of the suspending fluid in the gaps between the cell and the vessel wall. It is shown that the cell velocity and diameter of the capillary defines the value of the resistance of erythrocyte motion.

Blood Flow Velocity↗
PubMed1977

A mathematical model of microbial growth including an intermediate. I. Growth in batch cultures.

A mathematical model of microbial growth is presented and examined which, in contrast to the well-known MONOD model, includes transitions from one cell "bottle-neck" to another. This is achieved by introducing an intermediate product in the model. Three variants of the model for different regulatory functions of the intermediate are considered. The results permit to describe a set of experimentally observable microbial growth curves. According to the model, the shape of the growth curves, the kinetics of substrate consumption and changes of intermediate concentration depend on culture prehistory and the nature of the intermediate regulatory function.

Bacteria↗
PubMed1984

Operational research and cost containment: a general mathematical model of a workstation.

To facilitate planning and management, I have derived a mathematical model describing the dynamics of a workstation that receives a mixture of routine and emergency specimens. The model parameters include the maximal specimen-processing rate (to be defined by personnel representatives) and the longest delay allowed for emergency specimens at the workstation. Based on the model, a computer-simulation technique has been developed to maximize the length of time (planned pauses) during which the workstation could be closed without causing undue delay of routine and emergency specimen results. The application of this technique is illustrated with real data, in which more than 50% of the specimens were emergency specimens. Three pauses, constituting 35% of working hours, could be introduced with a negligible impact on the turnaround time of emergency specimens (mean increase = 8 min). The model may also be used to derive, as a function of time of day, the largest extra workload that may be presented to a workstation without creating overwork. The workload could be increased by 45%, provided that all additional specimens arrived before noon.

Cancer Care Facilities↗
PubMed1983

[Mathematical model of transcapillary metabolism in patients with mitral valve insufficiency].

Application of a mathematical model of microhemocirculation enabled one to assess quantitatively the magnitude of transcapillary albumin metabolism and total hydraulic resistance of metabolic vessels, as well as the effect of geometric, biophysical and hemodynamic parameters on transport characteristics of the capillaries. Dramatic changes in transcapillary metabolism and in blood rheologic properties are classified with factors that determine the occurrence of postoperative complications in patients with mitral valve failure.

Capillary Permeability↗
PubMed1996

[A complex mathematical model of decompression based on biophysical and physiological characteristics].

In the devised integral mathematical model of decompression body tissues are expressed as sets of spectra of specific body tissue semi-saturation periods calculated from tissue circulation and corrected for gas diffusion through the skin. Values of permissible oversaturation were determined as a sum of critical and permissible supercritical oversaturations. The critical oversaturation of tissues is proportional to the cubic root from the ambient pressure, whereas the permissible supercritical oversaturation is a function of time constant of tissue desaturation and critical oversaturation. This decompression model incorporates specific models of tissue saturation and desaturation asymmetry due to difference in physical activities, ambient temperature and oxygen partial pressure in the breathing mixture during exposure and decompression. Besides, an equation to evaluate and control oversaturation in the combined venous blood was established and used in the model. Experiments showed that following decompression regimes calculated with this model, the level of gas formation in the combined venous blood was significantly lower than after application of decompression following similar regimes in the Diving Service Rules-85.

Biophysical Phenomena↗
PubMed1976

Electrocochleography by mathematical modelling.

The aim of this work is to critically review some of the classical electrocochleographic methods in accordance with the systems theory: (a) in describing, by means of mathematical models, the different parts of the auditory system concerned in the generation of stimulus-evoked signals; and: (b) in comparing the outputs of these models with the measurements of the cochlear potentials. It must be stated clearly that we realise that many of the conclusions drawn could be criticised, it is hoped that future research in the field with be stimulated by this work.

Adaptation, Physiological↗
PubMed1991

A mathematical model of mandibular protrusion.

Mathematical expressions were derived to describe the sagittal plane movements of the mandible. It was shown that mandibular rotation during protrusion was a function of incisor and condylar guidances, initial mandibular angulation, mandibular size, and the extent of the excursion. Cusp tip displacement and center of rotation calculation algorithms were also developed for the protrusive path.

Cephalometry↗
PubMed1979

A mathematical model for the 1973 cholera epidemic in the European Mediterranean region.

For the cholera epidemic that occurred in the European Mediterranean region in the summer of 1973, a simple deterministic mathematic model is proposed; it consists of a system of two ordinary differential equations which concern the evolution of the human infective population in a town community and of bacteria population in the sea. It is conjectured that the infection process obeys a non linear saturation-type law. A phase space analysis is performed for the system of equations. Conclusions are drawn which concern the evolution of the epidemic and which suggest some indications for the selection of public health policies. The validity of the model is compared with the available data for the town of Bari (Italy).

Cholera↗
PubMedDate not supplied

The influence of semicircular canal morphology on endolymph flow dynamics. An anatomically descriptive mathematical model.

The classic Steinhausen/Groen mathematical description of endolymph flow in a toroidal semicircular canal is extended to the case where the size, shape, and curvature of the canal lumen change continuously through the duct, utricle, and ampulla. The resulting second-order differential equation has three coefficients, unlike the equation of a torsion pendulum, which has only two. The salient anatomical parameters which determine endolymph motion are: the length of the central streamline occupying the center of the canal lumen; the area enclosed by this streamline as projected into the plane of rotation; the average inverse cross-sectional area of the lumen (taken around the central streamline); and the average inverse squared cross-sectional area, weighted by a local wall shape factor. These parameters are evaluated and the average displacement of the face of the cupula is estimated for the human, guinea pig, and rat, based on new anatomical data presented in companion papers. The model predicts that the dynamic range of human average cupula motion lies between 520 A and 10 microns.

Animals↗
PubMed1987

Implications of a mathematical model for the role of lymphocytes with different lifespans in the recovery from tolerance.

An extension of the mathematical model of immunological tolerance including two categories of B and T helper cells, each having a different lifespan, is presented. The simulated recovery from tolerance is compared with experimental data on B and T helper cell tolerance to human gamma globulin (HGG) induced in adult mice. The performed simulation runs suggest the conclusion that in this case it seems impossible to incorporate a high ratio of both, long-lived B cells and/or short-lived T helper cells, if good agreement with the available experimental data should be preserved.

Animals↗