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PubMed1988

[Parametric identification of mathematical models of population genetics taking into account the geographical dispersion in finite samples].

A method for parameter identification of population genetics' mathematical models, taking account of geographical disperse at limited samples of experimental data on mutant frequency values has been developed. The existence of the MLS (method of the least squares) estimations of the models' parameters studied has been proved, zero approach of the looked for estimations found and the iterative procedure of making them precise shown. A means of building up the a posteriori function of probability density of the zero and following approximations of the models' parameters is pointed out. The possibility of application of the proposed method to find estimations of mathematical models' parameters of population genetics, taking account of geographical disperse, has been shown on the particular example.

Animals↗
PubMed2002

A mathematical model of phase 2 reentry: role of L-type Ca current.

Phase 2 reentry (P2R) is known to be one of the mechanisms of malignant ventricular arrhythmias, especially those associated with Brugada syndrome. However, little is known about the underlying mechanism for P2R. Our aim in this study was to simulate P2R in a mathematical model to enable us to understand its mechanism and identify a potential therapeutic target. A mathematical model of the L-type Ca current was composed according to whole cell current data from guinea pig ventricular myocytes recorded at 37 degrees C. Our mathematical model was incorporated into the modified Luo-Rudy phase 2 model. We set a dispersion in transient outward current (I(to)) density within the theoretical fiber, composed of 80 serially arranged epicardial cells with gap junctions and then observed the P2R. The dispersion in I(to) density within an only 0.8-cm epicardial theoretical fiber generated P2R with our Ca channel but not with the original model. When the P2R developed in the theoretical fiber, the calculated extracellular field potential showed coved-type ST segment elevation. We succeeded in generating P2R in our model for the first time. The local epicardial P2R may contribute the genesis of coved-type ST segment elevation in the Brugada syndrome.

Action Potentials↗
PubMed2006

An opposite role for tau in circadian rhythms revealed by mathematical modeling.

Biological clocks with a period of approximately 24 h (circadian) exist in most organisms and time a variety of functions, including sleep-wake cycles, hormone release, bioluminescence, and core body temperature fluctuations. Much of our understanding of the clock mechanism comes from the identification of specific mutations that affect circadian behavior. A widely studied mutation in casein kinase I (CKI), the CKIepsilon(tau) mutant, has been shown to cause a loss of kinase function in vitro, but it has been difficult to reconcile this loss of function with the current model of circadian clock function. Here we show that mathematical modeling predicts the opposite, that the kinase mutant CKIepsilon(tau) increases kinase activity, and we verify this prediction experimentally. CKIepsilon(tau) is a highly specific gain-of-function mutation that increases the in vivo phosphorylation and degradation of the circadian regulators PER1 and PER2. These findings experimentally validate a mathematical modeling approach to a complex biological function, clarify the role of CKI in the clock, and demonstrate that a specific mutation can be both a gain and a loss of function depending on the substrate.

Animals↗
PubMed1991

[A mathematical model of the regulation mechanism of Ca2+ concentration in lens in vivo].

In order to elucidate the regulation mechanism of homeostasis on intracellular Ca2+ concentration in lens in vivo, the authors proposed a new mathematical model based upon the model of Ca2+ active transport. The mathematical model has new factors: Ca2+ efflux and Ca2+ influx across the cell membrane related to the difference between intracellular and extracellular Ca2+ concentration. Changes in intracellular Ca2+ concentration were investigated by numerical simulation using this model. Ca2+ efflux (active transport) is increased with intracellular Ca2+ concentration and their relationship corresponds to a Michaelis-Menten reaction. Ca2+ influx increases with the Ca2+ permeable coefficient of cell membrane. These results are consistent with the experimental results is a qualitative way and indicate that the model is suitable to elucidate the regulation mechanism of intracellular Ca2+ concentration. From the theoretical point of view, therefore, it is suggested that intracellular Ca2+ concentration may depend on two factors: one is the Ca2+ dependence of the Ca2+ active transport system, the other the Ca2+ permeability of the cell membrane.

Calcium↗
PubMed1980

[Mathematical model of the electrical field in ischemic hearts].

The distribution of injury potentials on the cardiac and thoracic surface has been simulated by means of a simple, two-dimensional mathematical model utilizing the solid angle theory. The endocardial, epicardial and thoracic surfaces were represented by three concentric circumferences with radius of 2, 3 and 8 cm; the calculations have been performed with a digital computer (PDP 11/40). Five groups of ischemias have been considered according to their geometrical characteristics: three groups of ischemias affecting the entire ventricular wall, one group of subepicardial and one of subendocardial ischemias. The distribution of epicardial potentials clearly indicated the axis of symmetry and the epicardial border of all the ischemias where such a border existed. Conversely, visual inspection of the curves depicting the distribution of precordial potentials enabled little or no insight to be gained into the location and geometry of the ischemic areas; however, the epicardial or endocardial borders of the ischemic region could be easily determined from precordial data by using the mathematical model. In conclusion, detailed mapping of precordial injury potentials make it possible to obtain significant information on the location and geometry of myocardial ischemias, provided a suitable mathematical model is available.

Coronary Disease↗
PubMed1993

A comparison of overall mathematical models of the cardiovascular system for simulating response to orthostatic stresses.

Although numerous mathematical models of the cardiovascular system (CVS) have appeared in the literature only a few of them are models of the entire system with detailed representation of the heart, the vasculature, and the control elements. Like all models of biological systems, these models vary in complexity, and most of them are stimulus- specific. Their ability to simulate with acceptable accuracy either responses over a wide range of the stimulus or responses to stimuli of similar kind has not been reported. In this paper, three mathematical models of the CVS are examined in terms of their response to different orthostatic stresses, namely, lower body negative pressure (LBNP), head-up tilt, and blood loss. The short-term orthostatic responses of the models are compared to available experimental data. The models are: (i) Croston and Fitzjerrell's for study of LBNP and head-up tilt response, (ii) Jaron et al.'s for study of +Gz response, and (iii) Pullen's for simulation of response to blood loss. We will henceforth refer to these models by the letters C, J, and P, respectively.

Hemorrhage↗
PubMed1998

Mathematical modeling and fluorescence imaging to study the Ca2+ turnover in skinned muscle fibers.

A mathematical model was developed for the simulation of the spatial and temporal time course of Ca2+ ion movement in caffeine-induced calcium transients of chemically skinned muscle fiber preparations. Our model assumes cylindrical symmetry and quantifies the radial profile of Ca2+ ion concentration by solving the diffusion equations for Ca2+ ions and various mobile buffers, and the rate equations for Ca2+ buffering (mobile and immobile buffers) and for the release and reuptake of Ca2+ ions by the sarcoplasmic reticulum (SR), with a finite-difference algorithm. The results of the model are compared with caffeine-induced spatial Ca2+ transients obtained from saponin skinned murine fast-twitch fibers by fluorescence photometry and imaging measurements using the ratiometric dye Fura-2. The combination of mathematical modeling and digital image analysis provides a tool for the quantitative description of the total Ca2+ turnover and the different contributions of all interacting processes to the overall Ca2+ transient in skinned muscle fibers. It should thereby strongly improve the usage of skinned fibers as quantitative assay systems for many parameters of the SR and the contractile apparatus helping also to bridge the gap to the intact muscle fiber.

Animals↗
PubMed1986

A mathematical model of survival kinetics. I. Theoretical basis.

A mathematical model of mortality and survival kinetics is proposed based upon the two main aspects of survival data, namely, the rate of vitality reduction with age and its statistical distribution. Certain mathematical assumptions are made on the time-course of both vitality and its distribution. Then, these two aspects are integrated in a single model which can be used to describe survivorship, cumulative mortality or dying. The model is capable of fitting empirical curves even at very advanced ages, where the widely used Gompertz law fails. Examples are provided, derived from populations having rather different lifespans such as rotifers, flies, rats and horses. The model maintains one of the most interesting characteristics of Gompertz law, namely, the possibility to estimate the 'design constant for longevity' relating maximum lifespan to one of the parameters of the model. It also has the potential characteristics enabling it to be used to judge the statistical significance of the difference between two empirical survival curves.

Aging↗
PubMed2005

Mathematical model of influenza A virus production in large-scale microcarrier culture.

A mathematical model that describes the replication of influenza A virus in animal cells in large-scale microcarrier culture is presented. The virus is produced in a two-step process, which begins with the growth of adherent Madin-Darby canine kidney (MDCK) cells. After several washing steps serum-free virus maintenance medium is added, and the cells are infected with equine influenza virus (A/Equi 2 (H3N8), Newmarket 1/93). A time-delayed model is considered that has three state variables: the number of uninfected cells, infected cells, and free virus particles. It is assumed that uninfected cells adsorb the virus added at the time of infection. The infection rate is proportional to the number of uninfected cells and free virions. Depending on multiplicity of infection (MOI), not necessarily all cells are infected by this first step leading to the production of free virions. Newly produced viruses can infect the remaining uninfected cells in a chain reaction. To follow the time course of virus replication, infected cells were stained with fluorescent antibodies. Quantitation of influenza viruses by a hemagglutination assay (HA) enabled the estimation of the total number of new virions produced, which is relevant for the production of inactivated influenza vaccines. It takes about 4-6 h before visibly infected cells can be identified on the microcarriers followed by a strong increase in HA titers after 15-16 h in the medium. Maximum virus yield Vmax was about 1x10(10) virions/mL (2.4 log HA units/100 microL), which corresponds to a burst size ratio of about 18,755 virus particles produced per cell. The model tracks the time course of uninfected and infected cells as well as virus production. It suggests that small variations (<10%) in initial values and specific rates do not have a significant influence on Vmax. The main parameters relevant for the optimization of virus antigen yields are specific virus replication rate and specific cell death rate due to infection. Simulation studies indicate that a mathematical model that neglects the delay between virus infection and the release of new virions gives similar results with respect to overall virus dynamics compared with a time delayed model.

Animals↗
PubMed1986

A mathematical model of heterogeneous behavior of single muscle fibres.

A mathematical model of contracting muscle fibre is studied. The model is composed of an array of segments placed in series; any segment has an elastic element (PEi) and a contractile element (CEi) that describes the cross bridge kinetics. The corresponding system of nonlinear partial differential equations of the model is analyzed. Existence, uniqueness and continuous dependence of the solution are proven.

Animals↗
PubMed1976

Mathematical modeling and the redesign of a teaching ambulatory clinic.

Mathematical modeling was utilized in the planning and decision-making process involved in reorganizing a teaching clinic to effect continuity of care. The model interrelated physicians, time and space, facilitating value judgments and decisions. After examining multiple model runs, the authors finally selected a per-clinic-session doctor mix of 5 interns, 2.3 residents, and 1.6 fellows. Group productivity by model simulation was 14.6 pts/hour, utilizing 10.1 rooms. Subsequently, 90 house officers were each assigned to the clinic one-half day a week on a continuing basis. Time-motion data, from 10 sessions five months after the change, showed that during one week 353 patients were seen at a rate of 13.9 patients per hour in the rooms and time available. The fact that the reorganization was successful and the outcomes remarkably similar to model predictions has engendered confidence in the role of modeling in the planning process.

Ambulatory Care↗
PubMed1999

Interactive mathematical models of subjective alertness and cognitive throughput in humans.

The authors present here mathematical models in which levels of subjective alertness and cognitive throughput are predicted by three components that interact with one another in a nonlinear manner. These components are (1) a homeostatic component (H) that falls in a sigmoidal manner during wake and rises in a saturating exponential manner at a rate that is determined by circadian phase during sleep; (2) a circadian component (C) that is a function of the output of our mathematical model of the effect of light on the circadian pacemaker, with the amplitude further regulated by the level of H; and (3) a sleep inertia component (W) that rises in a saturating exponential manner after waketime. The authors first construct initial models of subjective alertness and cognitive throughput based on the results of sleep inertia studies, sleep deprivation studies initiated across all circadian phases, 28-h forced desynchrony studies, and alertness and performance dose response curves to sleep. These initial models are then refined using data from nearly one hundred fifty 30- to 50-h sleep deprivation studies in which subjects woke at their habitual times. The interactive three-component models presented here are able to predict even the fine details of neurobehavioral data from sleep deprivation studies and, after further validation, may provide a powerful tool for the design of safe shift work and travel schedules, including those in which people are exposed to unusual patterns of light.

Algorithms↗
PubMed2006

The mathematical model of insulin desorption from the bioactive, fibrous artificial store.

The aim of this study was to study insulin desorption from fibrous insulin artificial store in vitro as well as in vivo, with the intention to define a mathematical model that would describe this process. Release profile of cylindrical fibrous matrixes for various insulin concentrations, desorption temperatures, time periods, and pH were presented. Change of insulin concentration in the fibers and the effect of insulin release were discussed. This model was also used to predict the optimal conditions of the release process. Possibility of predicting the effect of the fibrous store design parameters (fibre radius, amount of bonded insulin, fiber type) on the resulting insulin release rate was the major advantage of this mathematical model. Also, taking all the relevant conditions regarding these experiments into consideration, by the application of mathematical model, the diffusion coefficient during insulin release was determined.

Insulin↗
PubMed2002

A mathematical model of human atrioventricular nodal function incorporating concealed conduction.

This work develops a mathematical model for the atrioventricular (AV) node in the human heart, based on recordings of electrical activity in the atria (the upper chambers of the heart) and the ventricles (the lower chambers of the heart). Intracardiac recordings of the atrial and ventricular activities were recorded from one patient with atrial flutter and one with atrial fibrillation. During these arrhythmias, not all beats in the atria are conducted to the ventricles. Some are blocked (concealed). However, the blocked beats can affect the properties of the AV node. The activation times of the atrial events were regarded as inputs to a mathematical model of conduction in the AV node, including a representation of AV nodal concealment. The model output was compared to the recorded ventricular response to search for and identify the best possible parameter combinations of the model. Good agreement between the distribution of interbeat intervals in the model and data for durations of 5 min was achieved. A model of AV nodal behavior during atrial flutter and atrial fibrillation could potentially help to understand the relative roles of atrial input activity and intrinsic AV nodal properties in determining the ventricular response.

Atrial Fibrillation↗
PubMed2002

Contribution of a mathematical modelling approach to the understanding of the ovarian function.

The biological meaning of folliculogenesis is to free fertilisable oocytes at the time of ovulation. We approached the study of the control of follicular development at the level of follicular granulosa cells, on the experimental as well as mathematical modelling grounds. We built a mathematical model allowing for the processes of proliferation, differentiation and apoptosis. State variables correspond to the numbers of cells undergoing these different processes, while control variables correspond to the cellular transition rates. The model results raised the notion of proliferative resources, which leads to consider the optimal management of these resources and has motivated the settling of an experiment investigating the changes in the growth fraction within the granulosa throughout terminal development. We are now investigating the way gonadotrophins, and especially FSH, operate on granulosa cells, in order to account for the hormonal control of the divergent commitment of granulosa cells towards either proliferation, differentiation or apoptosis. We are thus focusing on the dynamics of cAMP production, which appears to be a keypoint in FSH signal transduction.

Animals↗
PubMed2006

Program design based on a mathematical model using rating of perceived exertion for an elite Japanese sprinter: a case study.

We investigated the effects of program design on 400-m sprint time by applying a Rating of Perceived Exertion (RPE) mathematical model to training performance. The subject was 24 years old and had been training for 9 years. His best performance in 400-m sprint competitions was 45.50 seconds. Body weight, resting heart rate, training time and RPE were monitored daily after training sessions. Similarly, performance in 400-m races was recorded 9 times during 2003. At the World Championships in Athletics in France, the subject's team placed eighth in the 1,600-m relay. The RPE mathematical model was able to predict changes in performance. Rate of matching was statistically significant (r(2) = 0.83, F ratio = 34.27, p < 0.001). Application of the RPE mathematical model to the design of a training program specific to the needs of a 400-m sprinter indicates a potentially powerful tool that can be applied to accurately assess the effects of training on athletic performance.

Adult↗
PubMed1978

Systems-matching by degeneration. II. Interpretation of the generation and degeneration of retinal ganglion cells in the chicken by a mathematical model.

Quantitative data on generation and degeneration of retinal ganglion cells during development (Rager and Rager, 1978) are interpreted in terms of a mathematical model which consists of a system of differential equations. By these equations we attempt to describe the formation of retinal ganglion cells and their termination domains in the tectum. Since ganglion cells seem not to degenerate before their axons have arrived at their termination site and start branching, from the arrival time on they may become competent either to continue to mature or to die. Therefore, to find the actual number of competent cells the extension of the fiber pathway between the retina and the optic tectum had also to be measured and computed. The differential equations are united by the principle that at any given time cells in excess of the number of termination domains have to die. By this model the mathematical function was determined. Several parameter values of this function were optimized with the Gauss-Newton method by which the curve was fitted to the measured values. The high correlation obtained by this method allows to conclude that, to a first approximation, the model may be satisfactory. The evidence of competition for termination sites and of systems-matching by cell death is discussed.

Age Factors↗
PubMed2002

Quantitative assessment of agricultural runoff and soil erosion using mathematical modeling: applications in the Mediterranean region.

Three mathematical models, the runoff curve number equation, the universal soil loss equation, and the mass response functions, were evaluated for predicting nonpoint source nutrient loading from agricultural watersheds of the Mediterranean region. These methodologies were applied to a catchment, the gulf of Gera Basin, that is a typical terrestrial ecosystem of the islands of the Aegean archipelago. The calibration of the model parameters was based on data from experimental plots from which edge-of-field losses of sediment, water runoff, and nutrients were measured. Special emphasis was given to the transport of dissolved and solid-phase nutrients from their sources in the farmers' fields to the outlet of the watershed in order to estimate respective attenuation rates. It was found that nonpoint nutrient loading due to surface losses was high during winter, the contribution being between 50% and 80% of the total annual nutrient losses from the terrestrial ecosystem. The good fit between simulated and experimental data supports the view that these modeling procedures should be considered as reliable and effective methodological tools in Mediterranean areas for evaluating potential control measures, such as management practices for soil and water conservation and changes in land uses, aimed at diminishing soil loss and nutrient delivery to surface waters. Furthermore, the modifications of the general mathematical formulations and the experimental values of the model parameters provided by the study can be used in further application of these methodologies in watersheds with similar characteristics.

Agriculture↗