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At least 1,189 records · Page 66Linked to original sources
PubMed1980

A comprehensive mathematical model of stem cell proliferation which reproduces most of the published experimental results.

On the basis of experimental knowledge about haemopoietic stem cells a catalogue of fundamental statements is formulated. From this a simple mathematical model of haemopoietic regulation mechanisms is developed. The functional net effects of regulatory processes which are still unknown or unmeasurable are estimated using evolution arguments. The model is developed in three steps. It allows description of the self-replication of stem cells after direct destruction as well as their reaction to increased or reduced needs in the erythropoietic system. The most important experimental data about changes in CFUs, BFUe and CFUe after acute or chronic irradiation, anaemia, hypoxia, hypertransfusion or direct erythropoietic stimulation can be reproduced within the model. The model allows us to understand most of the results of experimental stem cell research. Furthermore, it can be applied for a more precise analysis of the existing data. Predictions about the results of certain experiments can be made.

Animals↗
PubMed1993

[Analysis of measuring conditions of surface electromyogram using mathematical model].

To study the measuring conditions of surface electromyogram for work analysis in the field of industrial health, the effect of electrode fixation, electrode distance and electrode-muscle distance were studied using a mathematical model. The results were as follows; 1) The output waveforms of two electrode fixed models, i.e., parallel-fixed model (two electrodes were fixed in parallel to the direction of the muscle fibers) and transverse-fixed model (two electrodes were fixed in transverse to the direction of the muscle fibers) were compared. The maximum output and rectified integrated output of the parallel-fixed model were 2.59 times and 1.2-1.5 times larger than those of transverse-fixed model, respectively. The high output area of the parallel-fixed model was only one round area, but the areas of transverse-fixed model were four round areas which were wider than the area of the parallel-fixed model. The rectified integrated output of the parallel-fixed model was more affected by the location of neuro-muscular junction than that of transverse-fixed model when the electrodes were fixed near the neuro-muscular junction. 2) The rectified integrated output increased by electrode distance, and the changing rate of the rectified integrated output by electrode distance was particularly large when the electrode distance was shorter than 2 cm.(ABSTRACT TRUNCATED AT 250 WORDS)

Electromyography↗
PubMedDate not supplied

Mathematical modeling of toxicity problems in aquaria.

The identification of an actual or potential toxicity problem in an aquatic system immediately poses several questions of practical importance. Is the toxic agent still being added to the system? Where is the toxin coming from? Are the current filtration systems removing it? How soon will it be reduced to an acceptable level? How can it be removed faster? These questions in turn suggest an equally important question. What samples should be examined? Analysis of animal tissues from bioassays is the most common investigative technique in use, but alternatives do exist. Testing of water has not been utilized to its fullest potential. The need for an orderly approach to sampling and interpretation has been a major factor in this under utilization. Mathematical modeling through the use of toxicokinetics can be used to maximize the efficiency of analysis of a toxic accident by water sampling. Strategies of sampling and interpretation of results will be discussed using the tools of toxicokinetic modeling.

Kinetics↗
PubMedDate not supplied

[Mathematical model of the cytokinetics of erythropoiesis in mouse bone marrow and spleen].

The described model approximates the function of the erythropoietic system of the mouse to the function of a self-renewed cellular system, describable in the terms of cell population kinetics. The model is based on a number of experimentally proved ideas of contemporary haematology and arises from the assumption that there exists mutual negative influence between the cellular populations of the bone marrow and spleen. Considering the erythropoietic system in the mouse to be composed of two relatively independent parts - the bone marrow and spleen - the described model differs from the attempts so far made on the mathematical modelling of erythropoiesis.

Animals↗
PubMed1971

A mathematical model of the controlled plant of the respiratory system.

Ability to predict the dynamic response of oxygen, carbon dioxide tensions, and pH in blood and tissues to abrupt changes in ventilation is important in the mathematical modeling of the respiratory system. In this study, the controlled plant (the amount and distribution of O(2) and CO(2)) of the respiratory system is modeled. Although the body tissues are divided into a finite number of "compartments" (three tissue groups), in contrast to earlier models, the blood and tissue gas tensions within each compartment are considered to be continuously distributed in time and in one spatial coordinate. The mass conservation equations for oxygen and carbon dioxide involved in the blood-tissue gas exchange are described by a set of partial differential equations which take into account convection of O(2) and CO(2) caused by the flow of blood as well as diffusion due to local tension gradients. Nonlinear algebraic equations for the dissociation curves, which take into account the Haldane and Bohr effects in blood, are used to obtain the relationships between concentrations and partial pressures. Time-variable delays caused by the arterial and venous transport of the respiratory gases are also included. The model so constructed successfully reproduced actual O(2) and CO(2) tensions in arterial blood, and in muscle venous and mixed venous blood when ventilation was abruptly changed.

Animals↗
PubMed1999

Kinetics of absorption atelectasis during anesthesia: a mathematical model.

Recent computed tomography studies show that inspired gas composition affects the development of anesthesia-related atelectasis. This suggests that gas absorption plays an important role in the genesis of the atelectasis. A mathematical model was developed that combined models of gas exchange from an ideal lung compartment, peripheral gas exchange, and gas uptake from a closed collapsible cavity. It was assumed that, initially, the lung functioned as an ideal lung compartment but that, with induction of anesthesia, the airways to dependent areas of lung closed and these areas of lung behaved as a closed collapsible cavity. The main parameter of interest was the time the unventilated area of lung took to collapse; the effects of preoxygenation and of different inspired gas mixtures during anesthesia were examined. Preoxygenation increased the rate of gas uptake from the unventilated area of lung and was the most important determinant of the time to collapse. Increasing the inspired O2 fraction during anesthesia reduced the time to collapse. Which inert gas (N2 or N2O) was breathed during anesthesia had minimal effect on the time to collapse.

Absorption↗
PubMed2003

Estimating tsetse population parameters: application of a mathematical model with density-dependence.

A density-dependent model is used to describe the dynamics of an open population of tsetse flies (Diptera: Glossinidae). Immigration (or emigration) takes place when the total population is below (or above) a biologically determined threshold value. The population is also subjected to birth and death rates, as well as to the risk of being trapped (continuously or intermittently). During trapping the population decreases toward a 'low' equilibrium population and when trapping ceases the population starts recovering and increases toward a 'high' equilibrium. The model is fitted using data collected on trapped flies in four experiments. The first one was conducted with 'intermittent trapping' (i.e. several trapping-recovery cycles) on Glossina fuscipes fuscipes Newstead in the Central African Republic (Bangui area). In the other experiments, trapping data on Glossina palpalis palpalis (Robineau-Desvoidy) was collected in 'aggregate' form over several days at a time. Two of these were in Congo-Brazzaville (Bouenza area) and one in the Ivory Coast (Vavoua focus). Estimates are derived for the low and high equilibrium values as well as the trapping rate. The estimated effect of sustained trapping is to reduce the population to low equilibrium values that are 85-87% lower than the levels without trapping. The effects of the natural intrinsic growth and of the migration flows cannot be estimated separately because in the model they are mathematically indistinguishable.

Animal Migration↗
PubMed2005

[Application of GIS and integrated mathematic models on estimating forest land wood productiveness and solar energy use efficiency].

Based on the meteorological elements observation and mountain soil survey in Fujian Province, this paper approached the application of geographic information system (GIS) and integrated mathematic models on estimating the grid wood productiveness and solar energy use efficiency (SEUE) of regional forest land. The results showed that there was a significant quadratic correlation of annual mean temperature, precipitation and total solar radiation energy(TSRE) with longitude, latitude and altitude, and their multiple correlation coefficients ranged from 0.692 to 0.981. The regional annual mean TSRE, temperature and precipitation could be well estimated by GIS and integrated models of quadratic tendency curve, and linear, quadratic and quartic inverse distance weighted interpolation. These annual means estimated by the models did not differ greatly from observed data, and the t test values were 1.29, 0.12 and 0.06, respectively. The grid wood productiveness and SEUE of regional forest land in Fujian could also be well estimated with the aid of GIS and integrated models, which ranged from 2.32 m3 x hm(-2) yr(-1) to 18.61 m3 x hm(-2) yr(-1) and from 0.11% to 0.91%, respectively.

Biomass↗
PubMed1984

Mathematical modeling of stimulus-secretion coupling in the pancreatic beta-cell. III. Glucose-induced inhibition of calcium efflux.

The inhibitory effect of glucose upon 45Ca efflux from prelabeled pancreatic islets was simulated in a mathematical model for Ca2+-cyclic AMP interaction in the process of glucose-induced insulin release. At variance with a previous interpretation, it was postulated that glucose inhibits 45Ca efflux by facilitating the uptake of the cation by the vacuolar system. The latter facilitation did not hinder glucose from provoking a rapid accumulation of cytosolic Ca2+ and, hence, insulin release. The postulated facilitation was also suitable in simulating the effect of glucose upon 45Ca efflux, uptake, and intracellular distribution in the pancreatic islets.

Animals↗
PubMed1994

Mathematical model of cardiovascular mechanics for diagnostic analysis and treatment of heart failure: Part 1. Model description and theoretical analysis.

The planning of drug therapy for heart failure should involve both the diagnostic analysis of the patient's defective state and a prediction of the drug effects on the identified state. We have devised a mathematical model of cardiovascular system mechanics, on which both quantitative diagnosis and evaluation of drug effects can be made. The model was composed of systemic and pulmonary circulatory networks including the dynamics of the left and right ventricles. The model of the ventricles can represent both systolic and diastolic problems in heart failure through the parameters of ventricular contractility and diastolic stiffness. Each vascular network was composed of arterial and venous resistances and total vascular capacitance. Patient's ventricular and vascular parameters were estimated simultaneously from the clinically measurable haemodynamic variables based on the model. Despite the simplicity of the model, the results showed good agreement with clinical and experimental data. The clinically significant haemodynamic classification of heart failure by Forrester et al. (Forrester et al., 1977) was simulated well by the model. This model provides a useful basis for analysing pathophysiological states in heart failure and evaluating drug effects on the disease.

Heart↗
PubMed1997

Liquid ventilation: a mathematical model of gas diffusion in the premature lung.

The liquid ventilation (LV) technique was previously demonstrated to be a valuable alternative to ordinary gas ventilation, particularly for newborn patients with severely distressed lungs. This work describes a mathematical model of gas transfer phenomena occurring within the lungs of a preterm newborn baby ventilated with liquid perfluorocarbon (PFC) RM-101. The model was conceived in order to perform computer simulations of LV treatments. Its input parameters are tidal volume, respiratory frequency, oxygen and carbon dioxide tension in inlet PFC; its output data are the partial pressures of respiratory gases in the alveolar environment. Such values may be evaluated at any instant from the beginning of the treatment, in order to judge whether the therapy is able to meet the necessary conditions to arterialize properly the patient's venous blood. The model also enables optimisation procedures to be defined and performed. Quantitative results and graphs are supplied, with reference to the simulation of LV applied to a preterm newborn of 28 gestational weeks. The main results point out that a relatively short duration of initial transients is attainable (200 to 240 s) and that blood arterialization is possible even with low oxygen tension in inlet PFC (29.7 kPa (223 mmHg)).

Biomedical Engineering↗
PubMed1992

Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation.

An exact knowledge of the human fetus's respiratory mechanisms is still lacking; in particular, the role of human placental anatomy in oxygen exchange has not yet been studied satisfactorily. In this paper, a mathematical model of placenta as O2 exchanger between maternal and fetal blood was developed; it led to the solution of equations based upon diffusion laws and the haemoglobin dissociation curve. Particular care was taken to represent the regimen of laminar motion or whirling into the capillaries. Theoretical results were compared, under physiological conditions, with clinical data relating to fetal oxygenated blood p O2 during the second half of gestation (20th-38th weeks), and a theoretical confirmation of the decreasing effectiveness of placental O2 exchange during gestation was found. The result was able to describe oxygen exchange during a period in which clinical data are scanty (23rd-30th weeks). The effects of some pathological events on O2 exchange were then simulated. Model parameters were changed to simulate the effects on oxygen exchange of some typical pathological variations of placental anatomical features: exchange surface thickness and capillary length. The curves obtained for different gestational ages can easily be correlated with echographic measures of placental volume and dimensions of placental capillaries. The results also show that the human placenta is more sensitive to pathologies when it is young than at term of gestation.

Capillaries↗
PubMed1995

A mathematical model of flow through the terminal lymphatics.

Proper understanding of the mechanisms of fluid absorption and flow through the terminal lymphatics is essential for the control of several pathological conditions such as edema, bedsores and cancer. A mathematical model of the terminal lymphatics was developed using the principles of mechanics. Computer simulation results substantiate the hypothesis that fluid absorption and flow through the terminal lymphatics occur due to suction mechanisms of the adjacent contractile lymphatic segments and due to periodic fluctuations in the interstitial fluid pressure. In addition, the results suggested that increasing the length of a terminal lymphatic vessel beyond a certain limit does not cause further increase in fluid flow into the terminal lymphatic.

Biomedical Engineering↗
PubMed1996

Deterministic chaos in mathematical model of pacemaker activity in bursting neurons of snail, Helix pomatia.

Chaotic regimes in a mathematical model of pacemaker activity in the bursting neurons of a snail Helix pomatia, have been investigated. The model includes a slow-wave generating mechanism, a spike-generating mechanism, an inward Ca current, intracellular Ca ions, [Ca2+]in, their fast buffering and uptake by intracellular Ca stores, and a [Ca2+]in-inhibited Ca current. Chemosensitive voltage-activated conductance, gB*, responsible for termination of the spike burst, and chemosensitive sodium conductance, gNa*, responsible for the depolarization phase of the slow-wave, were used as control parameters. These conductances in intact snail bursting neuron are regulated by neuropeptides. Time courses of the membrane potential and [Ca2+]in were employed to analyse different regimes in the model. Histograms of interspike intervals, autocorrelograms, spectral characteristics, one-dimensional return maps, phase plane trajectories, positive Lyapunov exponent and especially cascades of period-doubling bifurcations demonstrate that approaches to chaos were generated. The bifurcation diagram as a function of gB* and the ([Ca2+]in-V) phase diagram of initial conditions reveal fractal features. It has been observed that a short-lasting depolarizing current of elevation of [Ca2+]in may evoke transformation of chaotic activity into a regular bursting one. These kinds of transitions do not require any changes in the parameters of the model. The results demonstrate that chaotic regimes of neuronal activity modulated by neuropeptides may play a relevant role in information processing and storage at the level of a single neuron.

Animals↗
PubMed1988

A three-dimensional mathematical model of the human masticatory system predicting maximum possible bite forces.

A three-dimensional mathematical model of the human masticatory system, containing 16 muscle forces and two joint reaction forces, is described. The model allows simulation of static bite forces and concomitant joint reaction forces for various bite point locations and mandibular positions. The system parameters for the model were obtained from a cadaver head. Maximum possible bite forces were computed using optimization techniques; the optimization criterion we used was the minimizing of the relative activity of the most active muscle. The model predicts that at each specific bite point, bite forces can be generated in a wide range of directions, and that the magnitude of the maximum bite force depends on its direction. The relationship between bite force direction and its maximum magnitude depends on bite point location and mandibular position. In general, the direction of the largest possible bite force does not coincide with the direction perpendicular to the occlusal plane.

Biomechanical Phenomena↗
PubMed1995

Mathematic modelling of the enteric nervous network. 5. Excitation propagation in a planar neural network.

A mathematical model of the enteric nervous system (Auerbach's plexus) as a planar neural network has been developed, based on the actual morphological data of its organization. The network is composed of excitatory (cholinergic) and inhibitory (adrenergic) neurones interconnected by polysynaptic channels, formed of the geometrically non-uniform unmyelinated nerve axons. The synaptic zones are modelled as a three-compartment open pharmacokinetics system, i.e., presynaptic terminal, synaptic cleft and postsynaptic membrane where the pharmacokinetic mechanisms of electrochemical coupling are considered. All the chemical reactions of transformation of acetylcholine and adrenaline within them are described by first order Michaelis-Menten kinetics. The propagation of the electrical impulse along the pathways and in the vicinity of the nerve terminal is described by the modified Hodgkin-Huxley equations. The results of numerical simulation of the propagation of excitation within the neuronal chain, inhibitory feedback circuit, and a planar neuronal network under normal physiological conditions and after treatment with cholinergic/adrenergic agonists and antagonists are presented. The model predicts the dose-dependent influence of pharmacological agents on the neural network function.

Action Potentials↗