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 37 records · Page 2Linked to original sources
PubMed1987

Enhancement of neutrophil-mediated phagocytosis by human granulocyte-macrophage colony-stimulating factor demonstrated using a novel mathematical model.

A mathematical model is presented which may be applied to describe and analyse data from microscopic phagocytosis assays. The method has been used to investigate the phagocytosis of opsonized yeast by peripheral blood neutrophils treated with purified recombinant human granulocyte-macrophage colony-stimulating factor (rH GM-CSF) in vitro. Under limiting conditions of serum opsonization, rH GM-CSF decreased the proportion of non-phagocytic cells and increased the mean number of ingested yeast per cell. Stimulation of phagocytosis was dose-dependent and occurred with concentrations of rH GM-CSF in the range 10-320 units/ml. The effect was dependent on a heat-labile component in serum and was not attributable to endotoxin contamination of the preparation.

Colony-Stimulating Factors↗
PubMed1985

Asbestos body concentrations in human lung: predictions from asbestos body counts in tissue sections with a mathematical model.

A mathematical model for predicting the concentration (Nv) of asbestos bodies (AB) in human tissue from the count (No) of these bodies in planar tissue sections is presented. The result is the equation Nv = No/[0.54 X A X (La + t)], giving the concentration of AB in numbers per gram of wet lung tissue. La, the average length (in microns) of the AB, is specific for each case; A is the area (square millimeters) of the tissue counted, and t is the thickness of the section (in microns). This equation fits experimental digestion results to a multiplicative error factor of less than 3. When an estimate of La, such as 51.6 microns, is used, the equation is less accurate but probably sufficiently accurate for the screening of lung specimens.

Asbestos↗
PubMedDate not supplied

[The key role of fructose-2,6-bis-phosphate in the temporal organization of carbohydrate metabolism. An auto-oscillating mathematical model].

A mathematical model describing the periodical temporal organization of the open futile cycle fructose-6-phosphate in equilibrium fructose-1,6-bisphosphate (F6P in equilibrium F1,6P2) is investigated. The oscillations in this cycle are caused by the regulatory cycle F6P in equilibrium fructise-2,6-bisphosphate (F2,6P2), catalyzed by phosphofructokinase-2 (PFK-2) with a cascade of covalent chemical modification. The apparent product activation of PFK-2 by F2,6P2 together with the F2,6P2 outflux from the regulatory cycle create square-shaped oscillations in the concentration of F2,6P2, a powerful reciprocal regulator of the enzymes of the futile cycle F6P in equilibrium F1,6P2. Compared to the mechanisms of the autonomous regulation of the F6P in equilibrium F1,6P2 cycle suggested previously, the new one provides an excellent temporal separation of the glycolytic and gluconeogenic pathways and possesses a considerably larger region of existence of the self-oscillatory behaviour.

Carbohydrate Metabolism↗
PubMed1977

Carbon monoxide exchanges between the human fetus and mother: a mathematical model.

A mathematical model was developed to calculate maternal and fetal carboxyhemoglobin concentrations, [HbCO], as functions of time during and after exposure of the mother to various inspired CO concentrations. Effects of variation in alveolar ventilation rates, pulmonary and placental fiffusing capacities, cardiac output, endogenous carbon monoxide production and other factors were studied. Following a change in the inspired CO concentration, fetal HbCO lags behind maternal HbCO by several hours. During CO uptake, fetal HbCO eventually overtakes maternal, and approaches an equilibrium value as much as 10% higher than the mother's. During CO washout the fetal levels again lag behind the mothers. Results indicate that treatment of pregnant women who have elevated HbCO levels with 100% oxygen reduces the time necessary to reduce the maternal HbCO level as expected, but that the rate of fetal CO elimination is not increased as much as that of the mother. Changes in maternal and fetal HbCO were also calculated for a representative exposure to changing inspired CO levels produced by fluctuating levels of air pollution. Finally, the effects of carboxyhemoglobin on fetal oxygenation were studied, including the effects of high altitude and exercise.

Carbon Monoxide↗
PubMedDate not supplied

[Nerve impulse conduction along myelinated fibers while internodal vary (mathematical model)].

The mathematical model of a myelinated fibre (Hille, 1971) was used to study the dependence of the velocity of nerve impulse propagation (theta) and of some parameters of the action potential on the properties of internodes. Calculations have shown that with increasing of the length (L) of internodes over the range of 0.75-3 mm, theta rises and then declines; in the fibre with the external diameter, D = 14 mu the maximum of theta falls on L = 1.5 mm. With decreasing of d/D (d = internal diameter of the fibre) at expense of D (simulation of the myelin sheath thickening) theta grows up monotonically, while the safety factor N (defined as the ratio of the potential (V) in the 6th node to V in the 8th node at a moment when V in the 8th node reaches its maximum) rises steeply only up to d/D approximately 0.75; with further increasing of D, N increases insignificantly. The raising of the longitudinal resistance (ri + r0) leads to the gradual decrease of theta; at ri + r0 = 70 mohm/cm the nerve impulse propagation ceased. The estimation of the longitudinal resistance of the intercellular clefts suggests that in the nerve trunks with a compact packing of nerve fibres the flow of the local currents through the axoplasm of the neighbouring fibres is a prerequisite for impulse conduction. The possibility of electrical (electronical) interaction between the membranes of nodes and internodes has been studied. Calculations have shown that if the generation of a membrane potential in the internode were absent, the resting potential of the node would by 10 mv lower than the potential created by the nodal "generator".

Action Potentials↗
PubMed1992

Mathematical modelling and field trials of an inexpensive endoskeletal above-knee prosthesis.

The swing-phase motion of the shank of an above-knee prosthesis has been modelled mathematically. An inexpensive endoskeletal prosthesis was designed using the Jaipur foot and conduit pipes with a hinge joint for the knee. Results of field trials and the modelling indicate that a very simple above-knee prosthesis can give near normal gait at "normal" walking speeds on flat surfaces. The swing of the shank is most sensitive to the timing of toe-off.

Acceleration↗
PubMed1977

[Effect of NAD recirculation on the mechanism of ATP stabilization in cytoplasm. Mathematical models].

A mathematical model of the glycolytic system with the cytoplasmic coenzymes NAD+ and NADH as essential variables is proposed. It has been shown that any increase in the steady-state concentration of NADH will reduce the range of activity of the "generalized" ATPase, wherein the level of ATP is stabilized. Such a reduction in the range of ATP stabilization may be caused by an increasing rate of the pyruvate loss into non-glycolytic pathways, in particular, into mitochondria. This effect may be compensated by increasing oxidation of NADH by the dehydrogenases of H+-transferring cytosol-mitochondrial shuttles (malate-aspartate or alpha-glycerophosphate). The properties of the complete model were compared with those of its simplified version, which takes account only of the phosphotransferase reactions of glycolysis. The effects of various factors, which do not alter the level of NADH in the system, may be studied within the scope of the simplified model.

Adenosine Triphosphatases↗
PubMed1989

A mathematical model of erythropoiesis in mice and rats. Part 1: Structure of the model.

A mathematical model has been developed which describes the regulation of erythropoiesis in mice and rats. The main model assumptions are: (1) Regulation is mediated by erythropoietin (EPO). (2) The production of EPO depends exponentially on the tissue oxygen pressure (e.g. in the renal production sites). (3) There are sigmoidal dose-response curves relating the EPO concentration in the plasma to the mitotic activity of CFU-E and proliferative erythropoietic precursors. For maximum stimulation two to four additional mitoses may occur, while for an absent stimulus three to five mitoses may be omitted. (4) The normal precursor transit time of three to four days may be shortened by more than 50% during maximum stimulation. (5) The erythrocytes have a normal lifespan of 42-56 days, which may be reduced to 15-20 days under erythropoietic stimulation. Among these assumptions, the dose-response relationships between EPO and the mitotic activity of CFU-E and the proliferative erythropoietic precursors are the most important hypotheses of the model. This is the first of a series of three papers and gives a description of the mathematical formalism and the parameters used. In the subsequent papers computer simulations on erythropoietic stimulation and suppression are presented.

Animals↗
PubMed1979

[Kinetic study of a heterogeneous tumor cell population using a mathematical model].

A mathematical model of a heterogenous tumor as a system of interrelating cell populations is described, including a pool of quiescent cells, cell-to-cell variability in maturation rates, and cell migration from growth area to necrotic one. Computer simulation results are given, model labeled mitoses and labeled index curves for the Lewis carcinoma are compared with experimental data.

Animals↗
PubMedDate not supplied

Heat loss and blood flow during hyperthermia in normal canine brain. II: Mathematical model.

A mathematical model for heating and cooling during hyperthermia has been developed from an appropriate solution of a bioheat transfer equation. Predicted cooling rates obtained from the model have been compared with cooling rates obtained from experiments performed on both perfused and non-perfused normal canine brain tissue. The agreement between the predicted and observed cooling rates in non-perfused tissue is satisfactory (within 6-11 per cent) and provides confidence that the conduction process is being accurately represented. The model is then used to estimate the relative contribution of conductive and convective (blood flow) heat loss during cooling for the in vivo experiments. Estimates of blood flow dynamics are made from cooling data taken early and late in a heating course using the model to correct for conductive heat loss. Simplified forms of the bioheat transfer equation are examined. An adequate model for the observed cooling data is one that treats heat loss (both conduction and blood flow) as a heat sink (i.e. an effective perfusion model) rather than an effective thermal conductivity model.

Animals↗
PubMed1987

Biomathematics of intracranial CSF and haemodynamics. Simulation and analysis with the aid of a mathematical model.

A mathematical model of the isolated intracranial system including autoregulation of cerebral blood flow with the aid of a variable cerebrovascular resistance is described. The rate of formation of cerebrospinal fluid is assumed to depend on the regional blood flow through the choroid plexuses. This model is extended by cardiovascular components including the left ventricle of the heart, the aorta and the peripheral resistance. Additionally the model contains control circuits to simulate the short-time behaviour of the blood pressure regulation with the aid of the baroreceptor reflex. Disturbances of central regulation of blood pressure are simulated depending on changes of the regional blood flow through the brain stem. The application of the model is demonstrated by the analysis of the influence of arterial blood pressure upon the intracranial pulse pressure relationship (PPR) and upon the pressure response to a volume pressure test. Theoretical considerations and simulations reveal an opposite effect of arterial blood pressure (ABP) and its amplitude upon PPR. The ICP amplitude rises with decreasing ABP or increasing ABP amplitude. Breakpoints and other deviations from a linear PPR over the whole ICP range are studied by the analysis of the transfer function. The application of the model concerning parameter estimation methods is demonstrated and discussed. Simulations of rhythmic phenomena with the aid of the extended model point out possible approaches to quantitative descriptions of disturbances of central regulation.

Brain↗
PubMed1979

Drug elimination interactions: analysis using a mathematical model.

A mathematical model was developed to analyze the elimination kinetics of drug interactions in the rat. The model is based on physiological blood flow rates and organ weights and includes Michaelis-Menten equations for enzymatic processes which are involved in the elimination of the drug; competitive inhibition interactions are computed for shared pathways. Using data from the single drugs, the model can simulate the results of experiments of the acute warfarin-BSP interactions in rats.

Animals↗
PubMed1991

Optimal tumor targeting by antibodies: development of a mathematical model.

A mathematical model has been developed to optimize tumor targeting with labeled antibodies. The model is compartmental and nonlinear, incorporating saturable binding. Published parameter values have been used in the model, and the resulting stiff differential equations have been solved using FACSIMILE, a computer package that can simulate very stiff differential systems. Results show that successful tumor targeting depends on an optimal combination of antibody dose, affinity, and molecular size. The model has allowed an assessment to be made of the complicated and interrelated dynamic relationships that these factors have on tumor targeting. It has also offered an explanation for previously unsatisfactory results from tumor targeting with labeled antibodies. The structural identifiability of the model parameters is also analyzed and it is shown that, with the prior knowledge of some parameters which is likely in practice, the remaining model parameters are uniquely identifiable.

Algorithms↗
PubMed1991

Autocrine and paracrine growth factors in tumor growth: a mathematical model.

A mathematical model of tumor growth including autocrine and paracrine control has been developed. The model starts with the logistic equation of Verhulst: dV/dt = rV (1-V/K). Autocrine controls are described as modifiers of the Malthusian growth rate (r), while paracrine controls modify the carrying capacity (K) of the system. The control mechanisms are expressed in terms of "candidate" functions, which are based upon the dynamic distribution of TGF-alpha TGF-beta in the local tumor environment. Three paradigms of tissue growth have been modeled: normal tissue wound repair, unrestricted, unperturbed tumor growth, and tumor growth in a (radiation) damaged environment (the Tumor Bed Effect, TBE). These scenarios were used to test the dynamics of the system against known phenomena. Computer simulations are presented for each case. The mode is being extended to include the description of heterogeneous tumors, within which subpopulations can express differential degrees of growth activity. Heterogeneous tumor models, with and without emergent subpopulations, and models of terminal differentiation are also discussed.

Animals↗
PubMed1987

Screening for colorectal cancer in a high-risk population. Results of a mathematical model.

A mathematical model was used to estimate the cost-effectiveness of colorectal cancer screening strategies for people who are at high risk because of a first-degree relative with colorectal cancer. The model uses indirect evidence about such factors as cancer incidence, sensitivity and specificity of different tests, and treatment effectiveness. The analysis indicates that for screening people over 40 yr old an annual fecal occult blood test may reduce colorectal cancer mortality by about one-third, either colonoscopy or barium enema may reduce mortality by approximately 85%, a 3-5-yr frequency for endoscopies or barium enemas preserves 70%-90% of the effectiveness of an annual frequency, and beginning screening at age 50 reduces effectiveness by 5%-10%. Although both barium enemas and colonoscopies appear to be effective in reducing mortality, the lower cost of the barium enema makes it a more cost-effective strategy. All of these estimates depend on the baseline estimates of each of the factors incorporated in the model; the conclusions are most sensitive to assumptions about the natural history of adenomatous polyps, the bleeding of adenomas and presymptomatic cancers, and the sensitivity of the fecal occult blood test. Recommendations about colorectal cancer screening must also consider factors such as discomfort, inconvenience, and the availability of various technologies.

Colonic Neoplasms↗
PubMed1988

The rate of gas-bubble growth in tissue under decompression. Mathematical modelling.

A mathematical model simulating the formation of gas bubbles in biological tissues under decompression is presented. It is written as a system of partial differential equations solved on a computer. For the nitrogen-oxygen gas mixture, used for respiration in deep-water immersions, the effects of the physico-chemical properties of the gases, the magnitude of pressure differentials and the density of bubble-formation centres on the bubble size and rate of growth were studied. It is shown that in the case of drastic pressure differentials the formation of bubbles capable of producing microcirculatory disturbances is accomplished within a few seconds.

Carbon Dioxide↗
PubMed1990

Doppler waveform pulsatility index and resistance, pressure and flow in the umbilical placental circulation: an investigation using a mathematical model.

A mathematical model of the umbilical placental circulation was used to examine the effect of different physiological variables on the pulsatility index (PI) of the umbilical artery Doppler waveform. The variables include the umbilical and placental resistances, the volume flow rate and the pressure. In the model the branching structure of the placental villous tree is considered in detail, while each arterial branch is itself represented simply using a resistor and a capacitor. Placental vascular disease is modelled as obliteration of a fraction of the terminal branches of the tree. The model umbilical artery PI depends on the ratio of the placental resistance to the umbilical artery resistance. The PI increases with vascular disease, but the rate of increase is not uniform. Initially, the placental resistance and the PI increase very slowly with vessel obliteration. Once the level of vessel obliteration has reached a large enough value--typically between 60% and 90% obliteration--the PI begins to rise sharply. A larger placental vascular bed can accommodate a greater level of vessel obliteration before this rapid PI rise begins. The umbilical artery PI also depends on the pulsatility of the input (aortic bifurcation) pressure waveform, but blood pressure variations in the physically attainable range cannot account for the very high PI values associated with fetal compromise. Physically attainable pressure waveform changes would, however, enable the fetus with substantial placental vascular disease to maintain umbilical volume flow rate, and at the same time exhibit a raised umbilical artery PI value.

Blood Flow Velocity↗
PubMed1988

Interrelations between glycolysis and the hexose monophosphate shunt in erythrocytes as studied on the basis of a mathematical model.

A mathematical model is presented which comprises the reactions of glycolysis, the hexose monophosphate shunt (HMS) and the glutathione system in erythrocytes. The model is used to calculate stationary and time-dependent metabolic states of the cell in vitro and in vivo. The model properly accounts for the following metabolic features observed in vitro: (a) stimulation of the oxidative pentose pathway after addition of pyruvate due to a NADP-dependent lactate dehydrogenase as coupling enzyme between glycolysis and the oxidative pentose pathway, (b) relative share of the oxidative pentose pathway in the total consumption of glucose amounting to approximately 10% in the normal case and to approximately 90% under conditions of oxidative stress excreted by methylene blue. From the application of the model to in vivo conditions it is predicted that (c) under normal conditions glycolysis and the HMS are independently regulated by the energetic and oxidative load, respectively, (d) under conditions of enhanced energetic or oxidative load both glycolysis and the HMS are mainly controlled by the hexokinase; in this situation the highest possible values of the energetic and oxidative load which are compatible with cell integrity are strongly coupled and considerably restricted in comparison with the normal case, (e) the stationary states possess bifurcation points at high and low values of the energetic load.

Energy Metabolism↗