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 1,207 records · Page 67Linked to original sources
PubMed2004

A mathematical model of the methionine cycle.

Building on the work of Martinov et al. (2000), a mathematical model is developed for the methionine cycle. A large amount of information is available about the enzymes that catalyse individual reaction steps in the cycle, from methionine to S-adenosylmethionine to S-adenosylhomocysteine to homocysteine, and the removal of mass from the cycle by the conversion of homocysteine to cystathionine. Nevertheless, the behavior of the cycle is very complicated since many substrates alter the activities of the enzymes in the reactions that produce them, and some can also alter the activities of other enzymes in the cycle. The model consists of four differential equations, based on known reaction kinetics, that can be solved to give the time course of the concentrations of the four main substrates in the cycle under various circumstances. We show that the behavior of the model in response to genetic abnormalities and dietary deficiencies is similar to the changes seen in a wide variety of experimental studies. We conduct computational "experiments" that give understanding of the regulatory behavior of the methionine cycle under normal conditions and the behavior in the presence of genetic variation and dietary deficiencies.

Animals↗
PubMed2003

A mathematical model of the electrophysiological alterations in rat ventricular myocytes in type-I diabetes.

Our mathematical model of the rat ventricular myocyte (Pandit et al., 2001) was utilized to explore the ionic mechanism(s) that underlie the altered electrophysiological characteristics associated with the short-term model of streptozotocin-induced, type-I diabetes. The simulations show that the observed reductions in the Ca(2+)-independent transient outward K(+) current (I(t)) and the steady-state outward K(+) current (I(ss)), along with slowed inactivation of the L-type Ca(2+) current (I(CaL)), can result in the prolongation of the action potential duration, a well-known experimental finding. In addition, the model demonstrates that the slowed reactivation kinetics of I(t) in diabetic myocytes can account for the more pronounced rate-dependent action potential duration prolongation in diabetes, and that a decrease in the electrogenic Na(+)-K(+) pump current (I(NaK)) results in a small depolarization in the resting membrane potential (V(rest)). This depolarization reduces the availability of the Na(+) channels (I(Na)), thereby resulting in a slower upstroke (dV/dt(max)) of the diabetic action potential. Additional simulations suggest that a reduction in the magnitude of I(CaL), in combination with impaired sarcoplasmic reticulum uptake can lead to a decreased sarcoplasmic reticulum Ca(2+) load. These factors contribute to characteristic abnormal [Ca(2+)](i) homeostasis (reduced peak systolic value and rate of decay) in myocytes from diabetic animals. In combination, these simulation results provide novel information and integrative insights concerning plausible ionic mechanisms for the observed changes in cardiac repolarization and excitation-contraction coupling in rat ventricular myocytes in the setting of streptozotocin-induced, type-I diabetes.

Action Potentials↗
PubMed1989

A mathematical model for predicting relative muscle force with a perturbation analysis of selected muscle parameters.

A mathematical model is presented that predicts relative muscle forces using a minimum of experimentally derived input data. Tests of this model against literature values for maximum muscle force of four cat hindlimb muscles show a maximum error of only 5%. A perturbation analysis using this model demonstrates its sensitivity and applicability, as well as the congruence between this model and previous theoretical discussions of muscle function.

Algorithms↗
PubMed2001

A mathematical model of in vitro cancer cell growth and treatment with the antimitotic agent curacin A.

A mathematical model of cancer cell growth and response to treatment with the experimental antimitotic agent curacin A is presented. Rate parameters for the untreated growth of MCF-7/LY2 breast cancer and A2780 ovarian cell lines are determined from in vitro growth studies. Subsequent growth studies following treatments with 2.5, 25 and 50 nanomolar (nM), concentrations of curacin A are used to determine effects on the cell cycle and cell viability. The model's system of ordinary differential equations yields an approximate analytical solution which predicts the minimum concentration necessary to prevent growth. The model shows that cell growth is arrested when the apoptotic rate is greater than the mitotic rate and that the S-phase transition rate acts to amplify this effect. Analysis of the data suggests that curacin A is rapidly absorbed into both cell lines causing an increase in the S-phase transition and a decrease in the M-phase transition. The model also indicates that the rate of apoptosis remains virtually constant for MCF-7/LY2 while that of A2780 increases 38% at 2.5 nM and 59% at 50 nM as compared to the untreated apoptotic rate.

Antineoplastic Agents↗
PubMed2001

Mathematical model for evaluation of mass transfer limitations in phenol biodegradation by immobilized Pseudomonas putida.

A mathematical model is proposed to analyze the mass transfer limitations in phenol biodegradation using Pseudomonas putida immobilized in calcium alginate. The model takes into account internal and external mass transfer limitations, substrate inhibition kinetics and the dependence of the effective diffusivity of phenol in alginate gel on cell concentration. The model is validated with the experimental data from batch fermentation. The effect of various operating conditions such as initial phenol concentration, initial cell loading, alginate gel loading on the biodegradation of phenol is experimentally demonstrated. Phenol degradation time is found to decrease initially and reach stationary value with increase in cell loading as well as gel loading. The model predicts these trends reasonably well and shows the presence of external mass transfer limitations. A new concept of effectiveness factor is introduced to analyze the overall performance of batch fermentation.

Biodegradation, Environmental↗
PubMed2000

Mathematical modeling of air sparging for subsurface remediation: state of the art.

A review of published mathematical models used to simulate air sparging is provided. Applicability of the models, efforts to test the models using experimental data and contributions of modeling efforts to the practice of air sparging are also discussed. Compartmentalized lumped-parameter models and multiphase flow models have dominated air-sparging modeling efforts. In essence, each class of models requires the assumption of a continuum over some model domain. Each approach has significant benefits as well as some inherent disadvantages. Based on the literature, both lumped-parameter modeling and multiphase-flow modeling have been successful in improving our theoretical understanding of the air-sparging process and in facilitating practical development of sparging systems. Lumped-parameter models are simpler to use, and can lend considerable insight to sparging operations. Multiphase flow models have the potential to offer a more realistic simulation of the airflow process, but may require a considerable amount of data collection for model input. The literature suggests that for any air-sparging model to be useful for field applications, detailed model calibration is necessary. It is recommended that models incorporate, in some fashion, the diffusion and dispersion of contaminants to macro-scale air channels, and nonequilibrium interphase mass transfer of contaminants. These mass-transfer-limited processes are frequently listed as causes for the "tailing" of vapor-extraction effluent contaminant concentrations that are frequently observed during field applications. However, time-varying mixing of relatively clean and contaminated vapors in the extraction system may also explain this tailing. Geophysical imaging techniques and inverse modeling combined with air-sparging pilot tests and measurement of traditional hydrogeologic parameters may allow for successful modeling efforts.

Air↗
PubMed1990

Volume-activated chloride permeability can mediate cell volume regulation in a mathematical model of a tight epithelium.

Cell volume regulation during anisotonic challenge is investigated in a mathematical model of a tight epithelium. The epithelium is represented as compliant cellular and paracellular compartments bounded by mucosal and serosal bathing media. Model variables include the concentrations of Na, K, and Cl, hydrostatic pressure, and electrical potential, and the mass conservation equations have been formulated for both steady-state and time-dependent problems. Ionic conductance is represented by the Goldman constant field equation (Civan, M.M., and R.J. Bookman. 1982. Journal of Membrane Biology. 65:63-80). A basolateral cotransporter of Na, K, and Cl with 1:1:2 stoichiometry (Geck, P., and E. Heinz. 1980. Annals of the New York Academy of Sciences. 341:57-62.) and volume-activated basolateral ion permeabilities are incorporated in the model. MacRobbie and Ussing (1961. Acta Physiologica Scandinavica. 53:348-365.) reported that the cells of frog skin exhibit osmotic swelling followed by a volume regulatory decrease (VRD) when the serosal bath is diluted to half the initial osmolality. Similar regulation is achieved in the model epithelium when both a basolateral cotransporter and a volume-activated Cl permeation path are included. The observed transepithelial potential changes could only be simulated by allowing volume activation of the basolateral K permeation path. The fractional VRD, or shrinkage as percent of initial swelling, is examined as a function of the hypotonic challenge. The fractional VRD increases with increasing osmotic challenge, but eventually declines under the most severe circumstances. This analysis demonstrates that the VRD response depends on the presence of adequate intracellular chloride stores and the volume sensitivity of the chloride channel.

Animals↗
PubMed1996

Experimental verification of a mathematical model for pelleted growth of Streptomyces coelicolor A3(2) in submerged batch culture.

A published mathematical model for growth of pellets of filamentous microorganisms has been tested by comparison of model predictions with experimental data on growth of Streptomyces coelicolor in liquid batch culture. The original model considered the classification of pellets into a range of size classes. Growth resulted in movement of pellets to classes of increasing size, while shear forces produced mycelial fragments which entered the smallest size class, from which they grew to form further pellets. This model did not correctly describe changes in pellet size distributions during growth and was therefore modified in two ways. In the first, new pellets were assumed to be formed by the break-up, by shear forces, of existing pellets into two pellets of equal size, rather than removal of small hyphal fragments from the pellet surface. The second modification assumed that the outer shell of active mycelial biomass had a density less than 1 g cm-3 and that hyphal density within this shell decreased with distance from the pellet centre. The modified model generated predictions which agreed closely with experimental data on biomass concentration, pellet size distribution, pellet number and pellet radius during batch growth, thereby supporting the assumptions on which the model was based. The model did not accurately describe final biomass concentration, through lack of consideration of autolysis of mycelia at the centre of larger pellets in which growth was limited by diffusion of nutrients. Attempts to incorporate autolysis into the model improved prediction of biomass concentration but were not based on sound biological assumptions and increased the complexity of the model. Further experimental work is required for accurate description of the effects of autolysis on pellet growth.

Models, Theoretical↗
PubMed1991

A mathematical model of overall cerebral blood flow regulation in the rat.

In the present work a mathematical model of the cerebrovascular regulatory system in the rat is presented. The model, a generalization of our previous one, includes the reactivity of proximal segments of the cerebrovascular bed and the neurogenic and myogenic feedback regulatory mechanisms besides the action of chemical regulatory factors. The model is then used to analyze the interaction of mechanisms regulating cerebral blood flow in several conditions of physiological importance. In the first stage of the work we simulated experiments in which the neural fibers are cut and artificially stimulated with external means. According to experimental evidence, simulation results point out the existence of an escape of blood flow from stimulation. The model imputes this escape phenomenon to the antagonistic action of chemical factors working on the distal segments of the cerebrovascular bed. In a second stage, we studied the neurogenic mechanism action in a physiological closed-loop condition. With this general model, autoregulation to arterial pressure changes and postischemic reactive hyperemia have been analyzed. A comparison of simulation results with recent experimental data shows that the model is able to produce 60-70% of the experimental regulatory capacity of the cerebrovascular bed. However, some relevant discrepancies still exist between the model and the experimental results, especially as regards the dilatory capacity of small cerebral arterioles. These discrepancies underline the existence of further regulatory mechanisms working on the cerebrovascular bed, the nature of which must still be clarified.

Animals↗
PubMed1996

A mathematical model of glioma growth: the effect of extent of surgical resection.

We have developed a mathematical model based on proliferation and infiltration of neoplastic cells that allows predictions to be made concerning the life expectancies following various extents of surgical resection of gliomas of all grades of malignancy. The key model parameters are the growth rate and the diffusion rate. These rates were initially derived from analysis of a case of recurrent anaplastic astrocytoma treated by chemotherapies. Numerical simulations allow us to estimate what would have happened to that patient if various extents of surgical resection, rather than chemotherapies, had been used. In each case, the shell of the infiltrating tumour that remains after 'gross total removal' or even a maximal excision continues to grow and regenerates the tumour mass remarkably rapidly. By developing a model that allows the growth and diffusion rates to define the distribution of cells at the time of diagnosis, and then varying these rates by about 50%, we created a hypothetical tumour patient population whose survival times show good agreement with the results recently reported by Kreth for treatments of glioblastomas. Tenfold decreases in the rates of growth and diffusion mimic the results reported by many other investigators with more slowly growing gliomas. Thus, the model quantitatively supports the ideas that (i) gliomas infiltrate so diffusely that they cannot be cured by resection alone, surgical or radiological, no matter how extensive that may be; (ii) the more extensive the resection, regardless of the degree of malignancy of the glioma, the greater the life expectancy; and (iii) measurements of the two rates, growth and diffusion, may be able to predict survival rates better than the current histological estimates of the type and grade of gliomas.

Cell Division↗
PubMed1991

A mathematical model for the receptor mediated cellular regulation of the low density lipoprotein metabolism.

A prototype mathematical model for Brown and Goldstein's pioneering studies on the LDL receptor mediated pathway for the regulation of the cellular content of cholesterol has been developed in this paper. In order to analyze the essential features of this complex system quantitatively and still reflect the framework of the total system, six important processes are considered in the model. They are: (1A, B) the hydrolysis and synthesis of the LDL receptor; (2) the binding of LDL to its receptors; (3) the hydrolysis of LDL; (4) the storage of cholesteryl esters; (5) the regulation of de novo synthesis of cholesterol; and (6) the efflux of free cholesterol to the external medium. All these processes form a system to let the cells take up enough cholesterol from the external medium for their utilization and yet avoid the excessive accumulation of the lipid within the cells. The validity of the model is tested by showing that it can predict many of experimental curves obtained for human fibroblasts in tissue culture studies. The main purpose of the model is to determine how the free cholesterol level in the cell is related to the external LDL concentration and the regulatory capacity of the cells to adapt to a changing LDL environment. In addition, the model reveals an important behavior of SMC, i.e., for a slowly increasing LDL concentration in the extracellular medium, the rate of intracellular degradation of LDL will first increase and then become saturated. It is proposed based on these results that the saturation of LDL degradation by SMCs and the subsequent increase in subendothelial LDL levels in regions of high macromolecular permeability might play a vital role in the formation of the early foam cell lesion.

Cells, Cultured↗
PubMed2005

A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity.

In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1346-F1366, 2005), a region-based mathematical model was formulated for the urine concentrating mechanism (UCM) in the outer medulla (OM) of the rat kidney. In the present study, we quantified the sensitivity of that model to several structural assumptions, including the degree of regionalization and the degree of inclusion of short descending limbs (SDLs) in the vascular bundles of the inner stripe (IS). Also, we quantified model sensitivity to several parameters that have not been well characterized in the experimental literature, including boundary conditions, short vasa recta distribution, and ascending vasa recta (AVR) solute permeabilities. These studies indicate that regionalization elevates the osmolality of the fluid delivered into the inner medulla via the collecting ducts; that model predictions are not significantly sensitive to boundary conditions; and that short vasa recta distribution and AVR permeabilities significantly impact concentrating capability. Moreover, we investigated, in the context of the UCM, the functional significance of several aspects of tubular segmentation and heterogeneity: SDL segments in the IS that are likely to be impermeable to water but highly permeable to urea; a prebend segment of SDLs that may be functionally like thick ascending limb (TAL); differing IS and outer stripe Na(+) active transport rates in TAL; and potential active urea secretion into the proximal straight tubules. Model calculations predict that these aspects of tubular of segmentation and heterogeneity generally enhance solute cycling or promote effective UCM function.

Animals↗
PubMed1990

Erythrocyte sequestration and anemia in severe falciparum malaria. Analysis of acute changes in venous hematocrit using a simple mathematical model.

Microvascular erythrocyte sequestration, the characteristic pathological feature of falciparum malaria, was evaluated using a mathematical model in 46 patients with severe infections. From admission radioisotopic circulating red cell volumes and simultaneous venous hematocrits, the model-derived sequestrum hematocrit (mean [95% confidence limits]: 0.70 [0.43-0.97], n = 29) was twice that of peripheral blood (0.33 [0.30-0.36]). Serial reticulocyte and radiolabeled erythrocyte counts indicated that small numbers of cells enter the circulation during initial therapy. The mean fall in hematocrit over 84 h in 26 nontransfused patients conformed to a three-term equation. A first-order decline (t1/2 2.0 h [0.6-3.4]) suggested an average 7.5% plasma volume expansion through rehydration. A zero-order 6.3% (3.1-9.5) fall (t1/2 25.7 h [21.2-30.2]) occurred contemporaneously with a fall in mean parasitemia from 4.5% (3.6-5.4); from these data the model-derived average sequestered erythrocyte volume (4.8% of the admission hematocrit) was similar to the peripheral parasite burden. A second, first-order fall (t1/2 1,047 h [278-1,816]) indicated loss of uninfected erythrocytes with mean lifespan 62 d. Predicted total plasma volume expansion during initial therapy (21.2%) was similar to radioisotopic estimates in 11 patients (17.3% [2.0-33.1]). Application of the model to individual patient data showed wide variations in relative proportions of circulating and sequestered parasitized cells. The model provides evidence of the nature and fate of all parasitized erythrocytes in malaria.

Anemia↗
PubMed2000

Mathematical modeling of surface-active and non-surface-active drug transport in emulsion systems.

Mathematical models were developed for the prediction of surface-active and non- surface-active drug transport in triphasic (oil, water, and micellar) emulsion systems as a function of micellar concentration. These models were evaluated by comparing experimental and simulated data. Fick's first law of diffusion with association of the surface-active or complexation nature of the drug with the surfactant was used to derive a transport model for surface-active drugs. This transport model assumes that the oil/water (O/W) partitioning process was fast compared with membrane transport and therefore drug transport was limited by the membrane. Consecutive rate equations were used to model transport of non-surface-active drugs in emulsion systems assuming that the O/W interface acts as a barrier to drug transport. Phenobarbital (PB) and barbital (B) were selected as surface-active model drugs. Phenylazoaniline (PAA) and benzocaine (BZ) were selected as non- surface-active model drugs. Transport studies at pH 7.0 were conducted using side-by-side diffusion cells and bulk equilibrium reverse dialysis bag techniques. According to the surface-active drug model, an increase in micellar concentration is expected to decrease drug-transport rates. Using the Microsoft EXCEL program, the non-surface-active drug model was fitted to the experimental data for the cumulative amount of the model drug that disappeared from the donor chamber. The oil/continuous phase partitioning rates (k1) and the membrane transport rates (k2) were estimated. The predicted data were consistent with the experimental data for both the surface-active and non- surface-active models.

Algorithms↗
PubMed2001

A mathematical model of radiation carcinogenesis with induction of genomic instability and cell death.

We developed a mathematical model of carcinogenesis that incorporates genomic instability, a feature characterized by long-term destabilization of the genome in irradiated cells that leads to an increase in cancer risk in the exposed individuals at the cancer-prone age. This model also considers the induction of cell death, another important effect of radiation on cells. It is assumed that cell killing by radiation may occur at all stages of the carcinogenic process. The resulting model can explain not only the paradoxical relationship between low mutation rates and high cancer incidence but also the low-order dose-response relationship of cancer risk.

Apoptosis↗
PubMed2006

Mathematical model of the acute inflammatory response to Escherichia coli in intramammary challenge.

We constructed a mathematical model of the early response to Escherichia coli infection of the mammary gland and explored the roles and interactions between inflammatory cells and bacteria. The model incorporates 3 equations that describe the interactions among bacteria, milk somatic cells, and blood leukocyte densities. These 3 equations were fitted to cell densities observed during acute inflammatory responses in unvaccinated and vaccinated heifers inoculated with 10(4) or 10(6) cfu of E. coli. The rates computed for the cellular transit from the storage sites to the blood and from the blood to the milk were lower in cows receiving 10(4) cfu but increased at approximately 6 x 10(-6) and 30 x 10(-6) microL/cfu per h in nonvaccinated or vaccinated cows inoculated with 10(6) cfu, respectively. The cellular rates of bacterial killing were highest in unvaccinated cows ( approximately 400 x 10(-6) microL/cell per h) when compared with vaccinated cows (200 to 300 x 10(-6) microL/cell per h). A critical density of milk somatic cells at which bacteria density is constant was computed from the model at 2 x 10(6) cells/mL, and a one-way sensitivity analysis revealed that the changes in milk cellular densities were mostly sensitive to variations in the rate of bacterial killing and in the rate of production of inflammatory cells.

Animals↗
PubMed2000

Mathematical models behind advanced simulators in medicine.

The paper presents as an example the types of mathematical models that are used in a full scale anesthesia simulator. The models vary from detailed reference models, based on fundamental physiological laws and principles, to simple script based models. A few considerations on the implementation of the models are also given.

Anesthesiology↗
PubMed1988

The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS.

The role of mathematical models in the study of human immunodeficiency virus (HIV) transmission, the epidemiology and demographic impact of acquired immune deficiency syndrome (AIDS), and the course of infection within an individual is reviewed. Attention is focused on the part models can play in short-term prediction, parameter estimation, the interpretation of observed patterns, and the identification of areas in which knowledge is inadequate. Methods for short-term predictions, over 1-3 years, have proved reliable and can take account of distributed delays in the interval between reporting and diagnosis. Parametric and nonparametric methods have been developed for estimating summary statistics (e.g., means) for the distributed incubation period of AIDS. Current estimates, based on cohort or transfusion-associated AIDS cases, lie in the range of 7-10 years. Transmission models for longer-term prediction are less reliable at present given the many uncertainties concerning key epidemiological parameters. Theoretical studies highlight the need for quantitative data on temporal changes in the distribution of rates of sexual partner change and fluctuations in viral abundance in serum, secretions, and excretions (i.e., infectiousness) throughout the long and variable incubation period of the disease.

Acquired Immunodeficiency Syndrome↗