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At least 361 records · Page 20Linked to original sources
PubMed1991

Forecasting the number of future disabled elderly using Markovian and mathematical models.

The accuracy of forecasting the number of future disabled elderly people depends on the accuracy of projecting mortality rates and the rates of transition to and from functional disability. We describe a new two-step method for constructing mathematical models that project these future rates dynamically. (1) A Markovian model of elders' transitions between functional states is specified. (2) A mathematical model of the probability of each transition is created. We conducted pilot studies of the fundamental mathematical processes of this method using data from the Longitudinal Study of Aging. First we constructed prototypic mathematical models of the probabilities of remaining functionally able and of making transitions to disability and to death within 2 years. Then we used these models to project hypothetical rates of transition for white women of selected ages, morbidity ratings and health statuses.

Activities of Daily Living↗
PubMed2002

A new mathematical model quantifying drug release from bioerodible microparticles using Monte Carlo simulations.

PURPOSE: The major objectives of this study were to 1) develop a new mathematical model describing all phases of drug release from bioerodible microparticles; 2) evaluate the validity of the theory with experimental data; and 3) use the model to elucidate the release mechanisms in poly(lactide-co-glycolide acid)-based microspheres. METHODS; 5-Fluorouracil-loaded microparticles were prepared with an oil-in-water solvent extraction technique and characterized in vitro. Monte Carlo simulations and sets of partial differential equations were used to describe the occurring chemical reactions and physical mass transport phenomena during drug release. RESULTS: The new mathematical model considers drug dissolution, diffusion with nonconstant diffusivities and moving boundary conditions, polymer degradation/erosion, time-dependent system porosities, and the three-dimensional geometry of the devices. In contrast with previous theories, this model is able to describe the observed drug release kinetics accurately over the entire period of time, including 1) initial "burst" effects; 2) subsequent, approximately zero-order drug release phases; and 3) second rapid drug release phases. Important information, such as the evolution of the drug concentration profiles within the microparticles, can be calculated. CONCLUSIONS; A new, mechanistic mathematical model was developed that allows further insight into the release mechanisms in bioerodible microparticles.

Biotransformation↗
PubMedDate not supplied

[The use of mathematical modelling and prediction for assessing the efficacy of the treatment of periodontitis].

The statistical prediction and mathematical modelling techniques were applied to the analysis of the results of treatment of periodontitis. The afflicted focus cross-sectional area (as measured by X-ray film) was taken as a variable. A total of 40 patients were divided into 2 groups. Computer analysis allowed developing a mathematical model of the afflicted focus ossification under different therapeutical approaches.

Administration, Topical↗
PubMedDate not supplied

[The mathematical modelling of the displacement of the hard palate tissues in conservative uranoplasty].

Presents a mathematical model of sparing uranoplasty techniques developed by the authors; using this model, a physician may assess before surgery the volume of tissues needed to close the palatal defect. Experience gained with 72 surgeries carried out in children with unilateral cleft palate confirms the desirability of preliminary computations. Mathematical models for the most prevalent sparing uranoplasty methods are offered.

Child↗
PubMed2002

[The kinetic and mathematical model of PCR amplification experiment].

The PCR technique has been set up for nearly twenty years and is becoming more and more ripe. But because of the multiple influencing factors and complicated reaction procedures,no mathematical method that can describe the PCR reaction has been given. On the basis of its elementary principle,we suggested a kinetic equation to describe the reaction procedure,Wamp=[Ntarg x (1+P)n1+0.5 x Cenz x U x P x Ceactive x (n-nl)-Ntarg x (1+n x P)] x Cu x M. This equation can describe correctly the accumulation rule of PCR product and thus build up the kinetic-mathematical model of PCR reaction. The predicted CT value of PE 7700 by the kinetic-mathematical model was in accordance with the real value detected by the machine. This kinetic-mathematical model accompanied by proper detecting equipment and computer could make an automatic PCR instrument, which would produce much better result. A laboratory can predict the amount of PCR product by this model and provide accurate information for further handling of PCR product according to its own condition. In this model,the molecular basis that PCR reaction is doomed to change from exponential amplification to linear amplification had been clarified.

English Abstract↗
PubMedDate not supplied

[A mathematical model of the development of dental caries].

A mathematical model is suggested, simulating the development of carious process in a tooth, based on an analytical approach. The process of hydrogen ions diffusion into enamel microspaces is described via transport equation. A simplified model explaining the formation of the involvement of the body of the tooth under the enamel surface at the initial stages of caries development is described in detail. Analysis has shown that the theoretical model is in good correlation with experimental data on the rate of chemical reaction of Ca radionuclide accumulation in the enamel surface and deeper layers.

Dental Caries↗
PubMed1999

A mathematical model for the intracellular circadian rhythm generator.

A mathematical model for the intracellular circadian rhythm generator has been studied, based on a negative feedback of protein products on the transcription rate of their genes. The study is an attempt at examining minimal but biologically realistic requirements for a negative molecular feedback loop involving considerably faster reactions, to produce (slow) circadian oscillations. The model included mRNA and protein production and degradation, along with a negative feedback of the proteins upon mRNA production. The protein production process was described solely by its total duration and a nonlinear term, whereas also the feedback included nonlinear interactions among protein molecules. This system was found to produce robust oscillations in protein and mRNA levels over a wide range of parameter values. Oscillations were slow, with periods much longer than the time constants of any of the individual system parameters. Circadian oscillations were obtained for realistic values of the parameters. The system was readily entrainable to external periodic perturbations. Two distinct classes of phase response curves were found, viz. with or without a time domain within the circadian cycle in which external perturbations fail to induce a phase shift ("dead zone"). The delay and nonlinearity in the protein production and the cooperativity in the negative feedback (Hill coefficient) were for this model found to be necessary and sufficient to generate robust circadian oscillations. The similarities between model outcomes and empirical findings establish that circadian rhythmicity at the cellular level can plausibly emerge from interactions among molecular systems which are not in themselves rhythmic.

Biological Transport↗
PubMed2003

Validation of an original mathematical model of CO(2) elimination and dead space ventilation.

UNLABELLED: We present an original, mathematical model of ventilation and gas-exchange. Our aim was to validate it using data from previous clinical investigations, allowing our use of it in future investigations. The first previous investigation used a low-dead space, double-lumen, tracheal tube (DLT). We matched the model's PaCO(2) and airway pressures (P(AW)) to the patient mean during use of the DLT and a single-lumen tube (SLT). The model's resulting PaCO(2), PECO(2) and P(AW) were compared with the patients' as tidal volume (VT) changed with constant minute volume. The second investigation examined dead space during anesthesia. The model's VT, respiratory rate, CO(2) production, temperature, and alveolar and anatomical dead spaces were matched to each mechanically ventilated subject. Bias and precision in predictions of PaCO(2) and PECO(2) were calculated. The model's bias in prediction of dead space reduction by the DLT was 6.9%. Bias in prediction of P(AW) was 0.1% (peak) and -5.13% (mean), of PaCO(2) was 1.2% (DLT) and 1.5% (SLT) and of PECO(2) was 1.7% (DLT) and 1.3% (SLT). Prediction of PaCO(2) and PECO(2) in the second investigation (as 95% confidence interval of bias): PaCO(2) -2.6% to 0.8% and PECO(2) -4.9% to 1.2%. This validation allows future application of our model in appropriate theoretical investigations. IMPLICATIONS: We present an original, mathematical model of ventilation and gas exchange. We validate it against previously published clinical data to allow its use in future theoretical investigations where data may be unavailable from patients.

Airway Resistance↗
PubMed1982

A mathematical model of the Pacinian corpuscle.

This article describes a mathematical model of the Pacinian corpuscle based on the analysis of the available experimental data and on previous theoretical research. The model includes the main anatomofunctional constituents of the corpuscle: the capsula and the mechano-to-neural transduction; its structure accounts for the formation of the receptor potential and of the spikes on the nerve terminal. Comparison of the theoretical predictions with the experimental results, in response to different types of stimuli provides a substantial validation of the model and an explanation for the basic aspects of the transduction, in particular for: a) the receptor potential time course for isolated stimuli; b) the frequency response, in terms of receptor potential; c) the frequency threshold curve for the spikes; d) the firing rate, I.S.I. and P.S.T. histograms and the synchronization coefficient, in response to sustained sinusoidal inputs. Possible lines for future experimental research are suggested from the model predictions.

Electrophysiology↗
PubMed1983

[Mathematical models in hematology].

The use of mathematical models in haematology is shown by some examples concerning stem cell kinetics, erythropoiesis and thrombopoiesis. At first, model assumptions are formulated which include the biological knowledge and some regulatory hypotheses. Then, the reaction of the model on stimulation and suppression is calculated. Finally, by comparison with experimental or clinical data one can evaluate how far the model assumptions are sufficient to understand the measurements. Thus one can exclude wrong hypotheses and identify the important regulatory influences.

Blood Platelets↗
PubMed1978

A mathematical model for spreading cortical depression.

A mathematical model is derived from physiological considerations for slow potential waves (called spreading depression) in cortical neuronal structures. The variables taken into account are the intra- and extracellular concentrations of Na+, Cl-, K+, and Ca++, together with excitatory and inhibitor transmitter substances. The general model includes conductance changes for these various ions, which may occur at nonsynaptic and synaptic membrane together with active transport mechanisms (pumps). A detailed consideration of only the conductance changes due to transmitter release leads to a system of nonlinear diffusion equations coupled with a system or ordinary differential equations. We obtain numerical solutions of a set of simplified model equations involving only K+ and Ca++ concentrations. The solutions agree qualitatively with experimentally obtained time-courses of these two ionic concentrations during spreading depression. The numerical solutions exhibit the observed phenomena of solitary waves and annihilation of colliding waves.

Cortical Spreading Depression↗
PubMed1991

Pacemaker activity of the rabbit sinoatrial node. A comparison of mathematical models.

In the past decade, three mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed: the Bristow-Clark model, the Irisawa-Noma model, and the Noble-Noble model. In a comparative study it is demonstrated that these models, as well as subsequent modifications, all have several drawbacks. A more accurate model, describing the pacemaker activity of a single pacemaker cell isolated from the rabbit sinoatrial node, was constructed. Model equations, including equations for the T-type calcium current, are based on experimental data from voltage clamp experiments on single cells that were published during the last few years. In contrast to the other models, only a small amount of background current contributes to the overall electrical charge flow. The action potential parameters of the model cell, its responses to voltage clamp steps and its current-voltage relationships have been computed. The model is used to discuss the relative contribution of membrane current components to the slow diastolic depolarization phase of the action potential.

Action Potentials↗
PubMed2003

A numeric study of the noise-induced tremor in a mathematical model of the stretch reflex.

A mathematical model of the stretch reflex for the cat soleus muscle is presented. The time-delay differential equations of the model are solved using the fourth-order Runge-Kutta algorithm, introducing a Gaussian-noise term to simulate the environmental noise. The muscle response dynamics are then studied under various levels of average muscle activation. Finally, the feasibility of explaining the so-called physiological tremor from the properties of the stretch reflex mechanisms is discussed by comparing our results with reported experimental evidence.

Animals↗
PubMed1997

Fluid resuscitation following a burn injury: implications of a mathematical model of microvascular exchange.

A validated mathematical model of microvascular exchange in thermally injured humans has been used to predict the consequences of different forms of resuscitation and potential modes of action of pharmaceuticals on the distribution and transport of fluid and macromolecules in the body. Specially, for 10 and/or 50 per cent burn surface area injuries, predictions are presented for no resuscitation, resuscitation with the Parkland formula (a high fluid and low protein formulation) and resuscitation with the Evans formula (a low fluid and high protein formulation). As expected, Parkland formula resuscitation leads to interstitial accumulation of excess fluid, while use of the Evans formula leads to interstitial accumulation of excessive amounts of proteins. The hypothetical effects of pharmaceuticals on the transport barrier properties of the microvascular barrier and on the highly negative tissue pressure generated postburn in the injured tissue were also investigated. Simulations predict a relatively greater amelioration of the acute postburn edema through modulation of the postburn tissue pressure effects.

Burns↗
PubMed1998

Wear of polyethylene cups in total hip arthroplasty: a parametric mathematical model.

This paper presents a parametric mathematical model of the head-cup wear coupling in total hip arthroplasty (THA). The model evaluates the dependence of acetabular volumetric wear upon the characteristic parameters of patient and hip prosthesis. Archard's law is assumed to calculate the wear coupling behaviour. The wear factor is taken from pin-on-disc wear tests as a function of materials and finishing of the articular joint. The forces acting on the hip joint are taken from experimental data found in the literature whilst the load distribution is calculated under the hypotheses of perfectly rigid ideal wear coupling. The sliding distance is obtained by combining the three elementary displacements -- due to rotations around the three axes -- at the generic bearing surface location. The simulations show that the polymeric wear volume per step cycle decreases ranging from fast walking speeds to low running speeds, it increases linearly with patient body weight and with femoral head diameter, it decreases slightly for positive variations of the socket inclination angle and it increases exponentially with femoral head roughness. The volumetric wear rate per year calculated for a standard reference patient is 5.8 mm3. The relevant iso-wear maps show a marginal pattern with the maximum located near the cup superior borderline. At the instant of peak load, the iso-stress maps show a paracentral pattern with the maximum superior to the cup polar point, and the iso-sliding distance maps show a marginal pattern with two maxima located near the cup's superior and inferior borderlines.

Acetabulum↗
PubMed1999

A mathematical model of aerosol holding chambers.

A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above-mentioned factors, initial loss of aerosol by impact on the chamber wall is most important for the efficiency of a spacer. With a VT of 195 mL, the AeroChamber and Babyhaler were emptied in two breaths, the NebuChamber in four breaths, and the Nebuhaler in six breaths. Insufficiencies of the expiratory valves were demonstrated by comparison of pressure flow curves during "inspiratory" flow with and without occluded expiratory openings. Insufficient inspiratory valves were demonstrated by comparison of "expiratory" pressure flow curves with and without occluded inspiratory openings. With children breathing through the spacers, mask pressure variations were generally on the same order as that seen with the mechanical respiratory, supporting the clinical relevance of the in vitro findings.

Aerosols↗
PubMed2004

Elastic scattering and light transport in three-dimensional collagen gel constructs: a mathematical model and computer simulation approach.

A mathematical modeling approach for elastic scattering and light propagation is presented, which can be used to obtain the scattering coefficient, the index of refraction, and the distribution of the collagen fibrils in a gel. Collagen fibrils can be realistically represented by small cylindrical particles. The analysis of the scattering of light by such particles provides the scattering coefficient. Light transport in multilayered tissues has been modeled and the collagen fibrils scattering coefficient has been considered as main input parameters. Assuming that a gel is composed of fibrils with the same diameter, it is possible to obtain all the input parameters of the model and, therefore, a simulated spectrum. This can be repeated for several diameters. Considering a gel composed of fibrils with different diameters, it is possible to obtain a best-fitting simulated spectrum as a weighted sum (least-square-error based) of the spectra corresponding to several fibril diameters, and, therefore, obtain an estimate of the percentages of fibrils of each diameter in the gel. Moreover, the scattering coefficient and refractive index, which are also provided by the model, are relevant parameters as they relate to tissue properties in their own right.

Algorithms↗