Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Model”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,423 records · Page 79Linked to original sources
PubMed2005

Mathematical model that predicts isometric muscle forces for individuals with spinal cord injuries.

The ideal functional electrical stimulation (FES) system requires a mathematical model to provide feedforward control of the stimulation parameters such that they are optimal for different individuals across a range of physiological conditions, muscles, and tasks. Recently we tested and validated such a model using able-bodied subjects. The purpose of this study was to determine whether this model applied to persons with spinal cord injuries (SCI). To this end, the isometric force responses of the paralyzed quadriceps femoris muscles of 14 adolescents and young adults were tested. For each subject, the force responses to two six-pulse stimulation trains were used to identify the parameter values of the model and then the model was used to predict the force responses to three train patterns across a range of frequencies in both a nonfatigued and fatigued condition. The intraclass correlation coefficients (ICCs) between the experimental and predicted force-time integrals and peak forces were above 0.90 for 12 of the 13 stimulation trains tested in the nonfatigued condition and all 13 trains tested in the fatigued condition. The success of our model with SCI subjects leads us to believe that our model may be useful for designing optimal stimulation parameters for standing and ambulation in patients who use FES.

Adolescent↗
PubMed1996

Mathematical model of pacemaker activity in bursting neurons of snail, Helix pomatia.

On the basis of experimental data we have developed a mathematical model of pacemaker activity in bursting neurons of snail Helix pomatia which includes a minimal model of membrane potential oscillation, spike-generating mechanism, voltage- and time-dependent inward calcium current, intracellular calcium ions, [Ca2+]in, their fast buffering and accumulation, stationary voltage-dependent [Ca2+]in-inhibited calcium current. A resulting model of bursting pacemaker activity reproduces all experimental phenomena which were mimicked on the minimal model for membrane potential oscillation including (a) the effect of polarizing current on bursting activity, (b) an increase of input resistance during depolarizing phase, (c) induced hyperpolarization, etc. This model demonstrates adaptation of bursting activity to both the polarizing current and changes in the stationary sodium or potassium conductances. The model also reproduces the behavior of the transmembrane ionic current at membrane potentials clamped in different phases of slow-wave development; the calculated current-voltage relationships of the model neuronal membrane using a slow ramp potential clamp demonstrate hysteresis properties. Relationships between the model of bursting activity and the properties if intact bursting neurons are discussed.

Action Potentials↗
PubMed1982

Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: a theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias.

A mathematical model for the perturbation of a biological oscillator by single and periodic impulses is analyzed. In response to a single stimulus the phase of the oscillator is changed. If the new phase following a stimulus is plotted against the old phase the resulting curve is called the phase transition curve or PTC (Pavlidis, 1973). There are two qualitatively different types of phase resetting. Using the terminology of Winfree (1977, 1980), large perturbations give a type 0 PTC (average slope of the PTC equals zero), whereas small perturbations give a type 1 PTC. The effects of periodic inputs can be analyzed by using the PTC to construct the Poincaré or phase advance map. Over a limited range of stimulation frequency and amplitude, the Poincaré map can be reduced to an interval map possessing a single maximum. Over this range there are period doubling bifurcations as well as chaotic dynamics. Numerical and analytical studies of the Poincaré map show that both phase locked and non-phase locked dynamics occur. We propose that cardiac dysrhythmias may arise from desynchronization of two or more spontaneously oscillating regions of the heart. This hypothesis serves to account for the various forms of atrioventricular (AV) block clinically observed. In particular 2:2 and 4:2 AV block can arise by period doubling bifurcations, and intermittent or variable AV block may be due to the complex irregular behavior associated with chaotic dynamics.

Arrhythmias, Cardiac↗
PubMed2002

Analysis of a mathematical model for the growth of tumors under the action of external inhibitors.

In this paper we make rigorous analysis to a mathematical model for the growth of nonnecrotic tumors under the action of external inhibitors. By external inhibitor we mean an inhibitor that is either developed from the immune system of the body or administered by medical treatment to distinguish with that secreted by tumor itself. The model modifies a similar model proposed by H. M. Byrne and M. A. J. Chaplain. After simply establishing the well-posedness of the model, we discuss the asymptotic behavior of its solutions by rigorous analysis. The result shows that an evolutionary tumor will finally disappear, or converge to a stationary state (dormant state), or expand unboundedly, depending on which of the four disjoint regions Delta1,..., Delta4 the parameter vector (A1,A2) belongs to, how large the scaled apoptosis number;sigma is, and how large the initial radius R(0) of the tumor is. Finally, we discuss some biological implications of the result, which reveals how a tumor varies when inhibitor supply is increased and nutrient supply is reduced.

Animals↗
PubMed1982

Mathematical model of muscular fatigue. I. Metabolite level changes during exercises of different intensities.

To quantify muscular fatigue we study by a mathematical modelization the changes of the levels of ATP and various metabolites, and of the oxygen uptake with the intensity of a requested muscular exercise. The proposed model is consistent with the main phenomena experimentally observed during exercises; it allows also one to extrapolate these experimental results to any condition and to simulate exercise-complete and/or incomplete recovery cycles. The lactate kinetics allows one particularly to justify the empirical optimization of rest rhythms during exercises of long duration. Equations are solved using a 4th order Runge-Kutta method; computations are performed on an IRIS 80 CII computer.

Adenosine Triphosphate↗
PubMed1990

A mathematical model for the evolutions of anthelmintic resistance in a direct life cycle nematode parasite.

Some of the elements required of a mathematical model for the evolution of anthelmintic resistance in strongylid nematodes are described. The model comprises a series of coupled first order differential equations and assumes the parasite has a direct life cycle with overlapping generations. The parasite-host system involved only a single host. In all the cases considered, drug resistance was assumed to be determined by two alleles at a single autosomal locus. The pretreatment allelic frequencies were maintained by heterozygote advantage involving the mortality of the free-living stages of the parasite. The model suggests that alternating anthelmintic with different modes of action may be a less effective resistance management strategy than administering the same drugs simultaneously.

Animals↗
PubMed1985

Cardiovascular changes due to premature closure of the ductus arteriosus: a mathematical model.

Changes in the fetal cardiovascular system due to premature closure of the ductus arteriosus are described using a previously validated mathematical model. Results of the simulated closure of the ductus arteriosus are compared with reported results from animal experiments in which the ductus arteriosus was closed pharmacologically with prostaglandin synthetase inhibitors. The computed cardiovascular changes after ductus closure in the model resemble the changes obtained by administration of indomethacin. This suggests that the central cardiovascular effects of indomethacin (insofar as described here) can be completely attributed to closure of the ductus.

Animals↗
PubMed1996

Mathematical model for the combined effect of temperature and pH on the thermal resistance of Bacillus stearothermophilus and Clostridium sporogenes spores.

Two mathematical models have been studied to establish the relationship between the pH, treatment temperature and thermal destruction constant (k) of Bacillus stearothermophilus and Clostridium sporogenes spores. The study was carried out by heating the spores in mushroom extract acidified with two different acidulants (citric acid and glucono-delta-lactone). Among the models studied, the one that best described the inactivation was a second order polynomial equation, the precision of which depended on the microorganism studied.

Clostridium↗
PubMed2006

Mathematical modeling of flexural behavior of rotary nickel-titanium endodontic instruments.

The aim of the present study was to establish a mathematical model to characterize the flexural behavior of nickel-titanium (NiTi) rotary instruments. The bending behavior of ProFile (0.06 and 0.04 tapers), K-3 (0.06 taper), Quantec (0.04 taper) with tip size of ISO 25, was assessed by pressing the tip of the static rotary file against a smooth, freely movable, glass surface. The deflected instrument was photographed digitally, and the deflection path was digitized in software, to which data a function was fitted that best described the bending behavior of the instrument. It was found that all instruments deflected in a manner closely resembling a negative exponential function: y = A x e(-x/b). The present approach indicated that the analytical difficulties of handling the complex cross-section in tapering spirals in beam-bending theory may be circumvented by a practical and elementary curve-fitting method.

Dental High-Speed Equipment↗
PubMed2001

Mathematical modeling and stochastic H(infinity) identification of the dynamics of the MF-influenced oxidation of hexane.

This paper presents a mathematical model explicitly reflecting the magnetic-field-induced transitions in a biologically significant process: n-hexane oxidation. The range of the magnetic field strength is found (0.05-0.3 T) with the trend indicating significant magnetic-field-induced change in the rates of reactions involving hexane (up to 50% at 0.2 T). The equations describing the effects of the magnetic field on the photoinduced free radical reaction of oxidation involving a lipid-modeling substance, hexane, are obtained on the basis of chemical kinetics and data from a batch experiment. The magnetic-field-induced changes in n-hexane oxidation are validated using the identification technique based on the real time input-output data in a separately conducted flow-through experiment.

Hexanes↗
PubMed2003

An inverse algorithm for a mathematical model of an avian urine concentrating mechanism.

A nonlinear optimization technique, in conjunction with a single-nephron, single-solute mathematical model of the quail urine concentrating mechanism, was used to estimate parameter sets that optimize a measure of concentrating mechanism efficiency, viz., the ratio of the free-water absorption rate to the total NaCl active transport rate. The optimization algorithm, which is independent of the numerical method used to solve the model equations, runs in a few minutes on a 1000 MHz desktop computer. The parameters varied were: tubular permeabilities to water and solute; maximum active solute transport rates of the ascending limb of Henle and the collecting duct (CD); length of the prebend enlargement (PBE) of the descending limb; fractional solute delivery to the CD; solute concentration of tubular fluid entering the CD at the cortico-medullary boundary; and rate of exponential CD population decrease along the medullary cone. Using a base-case parameter set and parameter bounds suggested by physiologic experiments, the optimization algorithm identified a maximum-efficiency set of parameter values that increased efficiency by 40% above base-case efficiency; a minimum-efficiency set reduced efficiency by about 41%. When maximum-efficiency parameter values were computed as medullary length varied over the physiologic range, the PBE was found to make up 88% of a short medullary cone but only 8% of a long medullary cone.

Algorithms↗
PubMed2002

Mathematical modelling of MSW incineration on a travelling bed.

The rising popularity of incineration of municipal solid waste (MSW) calls for detailed mathematical modelling and understanding of the incineration process. In this paper, governing equations for mass, momentum and heat transfer for both solid and gaseous phases in a moving bed in a solid-waste incineration furnace are described and relevant sub-models are presented. The burning rates of volatile hydrocarbons in the moving bed of solids are limited not only by the reaction kinetics but also the mixing of the volatile fuels with the under-fire air. The mixing rate is averaged across a computation cell and correlated to a number of parameters including local void fraction of the bed, gas velocity and a length scale comparable to the particle size in the bed. A correlation equation is also included to calculate the mixing in the freeboard area immediately next to the bed surface. A small-scale fixed bed waste incinerator was built and test runs were made in which total mass loss from the bed, temperature and gas composition at different locations along the bed height were measured. A 2-D bed-modelling program (FLIC) was developed which incorporates the various sub-process models and solves the governing equations for both gases and solids. Thermal and chemical processes are mainly confined within a layer about 5-9 times in thickness of the averaged particle size in the burning bed. For a large part of the burning process, the total mass loss rate was constant until the solid waste was totally dried out and a period of highly rising CO emission followed. The maximum bed temperature was around 1200 K. The whole burning process ended within 60 min. Big fluctuations in species concentration were observed due to channelling and subsequent 'catastrophic' changes in the local bed conditions. Reasonably good agreement between modelling and measurements has been achieved. Yet the modelling work is complicated by the channelling phenomenon in the bed. Numerical simulations without consideration of the channelling effect produced very good agreement with experiments concerning the total mass loss, but significant discrepancy exists for temperature and gas composition profiles. Transient phenomena such as the breaking of waste particles and the "catastrophic" creation of new burning channels occurring during waste incineration is a vital area requiring further investigation at the fundamental level. The underlying theory of bed behaviour must be extended to include these transient events.

Disaster Planning↗
PubMed2003

Mathematical modelling of animate and intentional motion.

Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whether a particular human action should be captured in a single complex model or whether it is more promising to make extensive use of semantic knowledge and a collection of low-level models that encode certain motion primitives. Scene context plays a crucial role if we intend to give a higher-level interpretation rather than a low-level physical description of the observed motion. A semantic knowledge base is used to establish the scene context. This approach consists of three main components: visual analysis, the mapping from vision to language and the search of the semantic database. A small number of robust visual detectors is used to generate a higher-level description of the scene. The approach together with a number of results is presented in the third part of this article.

Computers↗
PubMed1998

Roles of calcium gradients in hyphal tip growth: a mathematical model.

A tip-high Ca2+ gradient is observed in growing fungal hyphae, but so far its role remains unknown. A mathematical model is presented, which provides evidence for the functions of such a Ca2+ gradient, in terms of its non-linear effect on the visco-elastic properties of the hyphal cytoskeleton. The model explains how the Ca2+ status at the tip may be responsible for the apical accumulation of vesicles and for an increase in the cytogel osmotic pressure, accompanied by the contraction of the cytoskeleton. The experimentally observed retraction of the spitzenkörper preceding the initiation of a branch is also reproduced, by simulating a subapical transient release of Ca2+ from internal stores.

Calcium↗
PubMed2006

Using mathematical modelling to inform on the ability of stormwater ponds to improve the water quality of urban runoff.

This paper concerns the mathematical modelling of flow and solute transport through stormwater ponds. The model is based on appropriate lumped system conservation equations that are solved using standard numerical techniques. The model was used to route a first flush pollution scenario through a cylindrical pond for 16 combinations of elevation and diameter of a submerged pipe outlet, in conjunction with a high level weir. Higher pipe elevations and smaller pipe diameters created larger pond volumes and hence led to greater dilution of the pollutant. In contrast, lower pipe elevations created larger storage volumes, leading to better flow attenuation. Interestingly, larger pipe diameters improved peak flow attenuation, even though the storage used decreased.

Cities↗
PubMed1976

Mathematical modeling of the mastitis infection process.

Mastitis infection is a biological process with a serial structure and stochastic in nature. A mathematical model for this process was developed from Markov chain theory. The unit of the process was an individual quarter; and four infection processes for first, second, third, fourth or higher lactation were described. Two Markov matrices which probabilistically determine the transitions between seven mutually exclusive states at each stage of the process were defined. After its validation, the model was used to determine the lactational consequences of the mastitis infection by calculating expected milk-yield productivity. Expected milk-yield productivity for an individual quarter was .93, .88, .85, and .84 for first, second, third, and fourth or higher lactation. The expected milk yield productivity of a quarter as a function of its state at the beginning of the process also was calculated. The quarters infected but not clinical have the lowest productivity.

Animals↗
PubMed1993

Mathematical model of the cut-off effect in the homologous series of tertiary amine local anesthetics.

It is proposed a simple mathematical model explaining the quasi parabolic dependence of the local anesthetic activity on the length of hydrophobic substituent in the homologous series of tertiary amines (TA). It is suggested that the molecules of TA intercalate between the lipid molecules in bilayers. Due to the mismatch between the lengths of lipid and TA hydrocarbon chains the intercalation results in a decrease in the bilayer thickness. The quasi parabolic dependence is the result of combination of partition equilibria and of geometrical parameters of interacting molecules in the bilayer. The model predicts that the TA chain length at which the maximum activity is observed should be dependent on the lipid: aqueous phase volume ratio. The empirical parameters used in the model are obtained from the X-ray diffraction on multilamellar egg yolk phosphatidylcholine (EYPC) dispersions with the monohydrochloride of [2-(heptyloxy)phenyl]-2-(1-piperidinyl)ethyl ester of carbamic acid and from the partition equilibria of its alkyloxy homologs with unilamellar EYPC liposomes.

Amines↗
PubMed1983

Simultaneous financial evaluation of a complex set of capital budgeting alternatives: a mathematical model.

Capital budgeting technics provide for financial evaluation of planned purchases of equipment or other major investments. In capital budgeting, the laboratorian often is faced with a complex set of alternatives, including leasing, installment purchasing, contracting work to another laboratory, and outright purchasing. This paper presents a mathematical model useful for simultaneously evaluating the financial worth of all such alternatives under the same set of assumptions. Armed with the results of financial evaluation and evaluations of quality, turnaround time, and other patient-care factors, the laboratorian can make better decisions regarding the choice of method which, in turn, will affect the productivity of the laboratory. The model is tended for application to mutually exclusive alternatives and includes three useful capital budgeting technics: (1) payback period, (2) net present value, and (3) profitability index. The technics are demonstrated as well as a method of programming the model in financial planning software for solution by microcomputer.

Budgets↗