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 1,171 records · Page 65Linked to original sources
PubMed2002

A mathematical model of rat collecting duct. II. Effect of buffer delivery on urinary acidification.

A mathematical model of the rat collecting duct (CD) is used to examine the effect of delivered load of bicarbonate and nonbicarbonate buffer on urinary acidification. Increasing the delivered load of HCO(3)(-) produces bicarbonaturia, and, with luminal carbonic anhydrase absent, induces a disequilibrium luminal pH and a postequilibration increase in urinary PCO2. At baseline flows, this disequilibrium disappears when luminal carbonic anhydrase rate coefficients reach 1% of full catalysis. The magnitude of the equilibration PCO2 depends on the product of urinary acid phosphate concentration and the disequilibrium pH. Thus, although increasing phosphate delivery to the CD decreases the disequilibrium pH, the increase in urinary phosphate concentration yields an overall increase in postequilibration PCO2. In simulations of experimental HCO(3)(-) loading in the rat, model predictions of urinary PCO2 exceed the measured PCO2 of bladder urine. In part, the higher model predictions for urinary PCO2 may reflect higher urinary flow rates and lower urinary phosphate concentrations in the experimental preparations. However, when simulation of CD function during HCO(3)(-) loading acknowledges the high ambient renal medullary PCO2 (5), the predicted urinary PCO2 of the model CD is yet that much greater. This discrepancy cannot be resolved within the model but requires additional experimental data, namely, concomitant determination of urinary buffer concentrations within the tubule fluid sampled for PCO2 and pH. This model should provide a means for simulating formal testing of urinary acidification and thus for examining hypotheses regarding transport defects underlying distal renal tubular acidosis.

Acids↗
PubMed1989

Mathematical model of the changes in heart rate elicited by vagal stimulation.

We developed a mathematical model of the underlying cellular mechanisms responsible for the changes in sinus cycle length (SCL) elicited by vagal stimulation in intact animals. The model incorporated a stimulation-mediated depletion of the releasable pool of acetylcholine (ACh) in the nerve endings, the in vitro reaction kinetics of acetylcholinesterase, and the electrical activity of a pacemaker cell with six membrane ionic currents. SCL increased linearly with the frequency of simulated vagal stimulation, as it does in animal experiments, because the concentration of ACh in the neuroeffector junction [( ACh]) saturated as the frequency of stimulation was increased and because SCL increased geometrically in response to increases in [ACh]. The dependence of SCL on the timing of vagal stimulation in the cardiac cycle resulted, in part, from the dependence of [ACh] on SCL. Simulated vagal stimulation entrained the sinus node because the rate of activation and inactivation of ACh-activated K+ channels depended only weakly on membrane potential during diastolic depolarization. SCL increased geometrically with [ACh], because 1) during diastolic depolarization, the amplitude of the ACh-activated K+ current was approximately equal to the amplitude of the sum of the other ionic currents, 2) [ACh] was low enough to saturate neither acetylcholinesterase nor the cellular system that activates the ACh-activated K+ channels, 3) the pacemaker cell membrane behaved electrotonically like a capacitor, and 4) the sum of all the ionic currents increased linearly with the amplitude of the ACh-activated K+ current.

Acetylcholine↗
PubMed2000

Technical note: The ability of mathematical models to describe the shape of lactation curves.

Seven of the best-known mathematical models based on least squares linear regression were fitted to data following the peaking (standard) lactation curve, termed type I, and a continuously decreasing lactation curve, termed type II. The Wood (1967) gamma function, the Cobby and Le du (1978) weighed least squares gamma function, quadratic and the Sikka (1950) model fitted to both types of curve. In contrast, the Jenkins and Ferrell (1984) and the inverse polynomial model always produced curves of type I, whereas the Brody et al. (1923) model always produced curves of type II. Data should be carefully examined to prevent the use of models unable to render the appropriate curve type described by yield data.

Animals↗
PubMed2001

Mathematical model of the male urinary tract.

The paper presents a simplified (but not trivial) mathematical model of the interaction between the urine flow and the male urethra and bladder, respectively. Urine is assumed to be a Newtonian fluid. The flow is considered to be non-stationary, isothermal and turbulent. The urethra and bladder wall, featuring elastic properties, experience large displacements and strains. The dynamic forces are included in the urethra wall motion. When fully extended the urethra attains the shape of an axisymetric tube. An iterative method based on the uncoupled approach is developed.

Diuresis↗
PubMed2000

Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair.

We develop a novel mathematical model for collagen deposition and alignment during dermal wound healing. We focus on the interactions between fibroblasts, modelled as discrete entities, and a continuous extracellular matrix composed of collagen and a fibrin based blood clot. There are four basic interactions assumed in the model: fibroblasts orient the collagen matrix, fibroblasts produce and degrade collagen and fibrin and the matrix directs the fibroblasts and determines the speed of the cells. Several factors which influence the alignment of collagen are examined and related to current anti-scarring therapies using transforming growth factor beta. The most influential of these factors are cell speed and, more importantly for wound healing, the influx of fibroblasts from surrounding tissue.

Cicatrix↗
PubMedDate not supplied

[Mathematical modeling of the process of thermal action of the surface of human skin].

The mathematical model of the physical system, which represents a pattern of a pulse heat source and a skin surface portion, is regarded as a dynamic process of thermal action on man. The model reflects a relationship of the parameters of a thermal pulse, the threshold characteristics of a thermoreceptor, and the thermal parameters of the skin.

Hot Temperature↗
PubMedDate not supplied

[Mathematical model of the digestion process regulation and its computer presentation].

The article presents a mathematic model, which describes regulation of the digestion process. The simulation was based on data on mutual influence of the factors participating in digestion regulation, which were acquired from analysis of over 1200 sources of experimental observations on digestion in dogs published in Russia and abroad, and on own experimental studies. The simulation includes 67 factors and about 400 interactions observed between them. The computer implementation of this simulation demonstrated descriptive coincidence of patterns of the variables respective to the factors of the model with experimental research data; the coincidence was observed in individual patterns and in combined patterns, as well as in coordinated responses in time.

Animals↗
PubMed2003

[A mathematical model of the functional state of the hemopoietic and erythropoietic system].

Proposed is a mathematical model of the functional state of the hemopoietic and erythropoietic systems in microgravity or long-term bed rest built on the principle of the minimal energy demand. Parameters of hematocrit, blood volume and minute blood volume in microgravity or long-term bed rest were determined. Results of model testing are in good agreement with the data about functioning of these systems in cosmonauts.

Blood Circulation↗
PubMed2004

Contact analysis and mathematical modeling of traveling wave ultrasonic motors.

An analysis of the contact layer and a mathematical modeling of traveling wave ultrasonic motors (TWUM) are presented for the guidance of the design of contact layer and the analyses of the influence of the compressive force and contact layer on motor performance. The proposed model starts from a model previously studied but differs from that model in that it adds the analysis of the contact layer and derives the steady-state solutions of the nonlinear equations in the frequency domain, rather than in the time domain, for the analyses of vibrational responses of the stator and operational characteristics of the motor. The maximum permissible compressive force of the motor, the influences of the contact layer material, the thickness of the contact layer, and the compressive force on motor performance have been discussed. The results show that by using the model, one can understand the influence of the compressive force and contact layer material on motor performance, guide the choice of proper contact layer material, and calculate the maximum permissible compressive force and starting voltage.

Journal Article↗
PubMed2004

A mathematical model to predict the release of water-soluble drugs from HPMC matrices.

A mathematical model to predict the fraction of water-soluble drug released as a function of release time (t, h), HPMC concentration (CH, w/w), and volume of drug molecule (V, nm3) was derived with ranitidine hydrochloride, diltiazem hydrochloride, and ribavirin as model drugs. The model is log (M(t)/M(infinity)) = 0.5 log t-0.3322CH-0.2222V-0.2988 (n = 140, r = 0.9848), where M(t) is the amount of drug released at time t, M(infinity) is the amount of drug released over a very long time, which corresponds in principle to the initial loading, n is the number of samples, and r is the correlation coefficient. The model was validated using isoniazid and satisfactory results were obtained. The model can be used to predict the release fraction of various soluble drugs from HPMC matrices having different polymer levels.

Algorithms↗
PubMed1991

A mathematical model describing the generation of oxygen radicals in mitochondria during ischemia-reperfusion.

A mathematical model for the generation of free radicals by mitochondria in ischemia-reperfusion is proposed. Computations show that normally two stable equilibrium states exist: the intact state, and the state characterized by damage to mitochondrial structures and a high rate of radical formation. Transition from one state to another occurs after hypoxia of a certain degree of severity and duration. The model also describes a number of phenomena observed during development of reperfusion injuries and drug therapy.

Free Radicals↗
PubMedDate not supplied

[Mathematical model of the dynamics of transport of inert gases in the microcirculatory system].

A mathematical model imitating transport of inert gases in the system of microcirculation under increased pressures was constructed. It has been shown that saturation of microareas nucleus of the brain cortex of average dimensions proceeds in about 90 sec. Effect of the blood flow velocity, gases tension in arterial blood and density of the capillary net on the dynamics of mass transfer of gases in a tissue was investigated.

Biological Transport↗
PubMedDate not supplied

[Myocardial parameters controlling vulnerability. Analysis of mathematical models].

Vulnerability induced by application of a properly timed premature stimulus was studied on mathematical models. Two mechanisms of vulnerability 1) reentry, 2) focal reexcitation were analysed. Tissue with a region of increased refractory period Rmax was simulated on Wiener's type model. The influence of high refractoriness region dimensions and tissue parameters on the duration of vulnarable period was studied. Reentry was shown to appear on the border of high refractoriness region, which minimal length lmin being the shorter, the greater was tau (maximal latency of response) and epsilon (epsilon = deltaR/R--degree of heterogeneity). The dependence of vulnerable period duration on current strength was computed for Nobel's model. The dip-phenomenon was found in this model, the vulnerable zone was located above the minimal value of threshold.

Animals↗
PubMed1995

Mathematical model of phagocytosis and inflammation after the inhalation of quartz at different concentrations.

A mathematical model was developed with several distinctive features to represent the various processes leading to silicosis. It assures the phagocytosis of quartz by the resident alveolar macrophages. It then models the necrosis of macrophages caused by the ingestion of quartz particles and the subsequent release of these clusters onto alveolar surfaces. The inflammatory recruitment of alveolar macrophages and neutrophils in response to the cell necrosis caused by the ingestion of quartz particles is described in a functional form and is included in the model. The model also describes the pathological and other biological reactions to quartz particles in the interstitium. Specifically, once the quartz particles arrive at the interstitium, they can be phagocytozed by interstitial macrophages. The pathological interaction between quartz and interstitial macrophages may lead to quartz particles being sequestered in silicotic nodules, and also cleared to the efferent lymph nodes.

Administration, Inhalation↗
PubMedDate not supplied

[A mathematical model of inhibition of the growth of Candida utilis by heavy metal ions].

A mathematical model described in this paper, contrary to other models, takes into account transport effects during penetration of the inhibitor into the cell of a micro-organism, and also a possibility of partial inactivation of the inhibitor during formation of complexes. It changes into models of Monod and Monod--Jerusalimsky at extreme values of parameters. Theoretical steady-state concentrations of the biomass in chemostat predicted on the basis of this model coincided with values obtained in experiments with limitation of growth of Candida utilis by silver ions and copper ions.

Candida↗
PubMed2002

Time-dependent transients in an ionically based mathematical model of the canine atrial action potential.

Ionically based cardiac action potential (AP) models are based on equations with singular Jacobians and display time-dependent AP and ionic changes (transients), which may be due to this mathematical limitation. The present study evaluated transients during long-term simulated activity in a mathematical model of the canine atrial AP. Stimulus current assignment to a specific ionic species contributed to stability. Ionic concentrations were least disturbed with the K(+) stimulus current. All parameters stabilized within 6-7 h. Inward rectifier, Na(+)/Ca(2+) exchanger, L-type Ca(2+), and Na(+)-Cl(-) cotransporter currents made the greatest contributions to stabilization of intracellular [K(+)], [Na(+)], [Ca(2+)], and [Cl(-)], respectively. Time-dependent AP shortening was largely due to the outward shift of Na(+)/Ca(2+) exchange related to intracellular Na(+) (Na) accumulation. AP duration (APD) reached a steady state after approximately 40 min. AP transients also occurred in canine atrial preparations, with the APD decreasing by approximately 10 ms over 35 min, compared with approximately 27 ms in the model. We conclude that model APD and ionic transients stabilize with the appropriate stimulus current assignment and that the mathematical limitation of equation singularity does not preclude meaningful long-term simulations. The model agrees qualitatively with experimental observations, but quantitative discrepancies highlight limitations of long-term model simulations.

Action Potentials↗
PubMed2004

[Mathematical modeling and simulation study of the heart rate feedback regulation system].

The physiological feedback regulation mechanism of the heart rate variation due to the blood pressure variation is studied. The continuous closed-loop mathematical model of the heart rate feedback regulation system is constructed. Numerical simulation is completed based on the above model. The simulation results demonstrate that the regulation system has the ability to constrain the fluctuation of the blood pressure to certain extent. The results are helpful for the pathological studies of some hypertensive diseases.

Blood Pressure↗
PubMed2006

Establishment of a discriminant mathematical model for diagnosis of deficiency-cold syndrome using gene expression profiling.

OBJECTIVE: To screen diagnostic markers of Deficiency-Cold syndrome by gene expression profile and to establish a discriminant mathematical milliliters model for the clinical diagnosis of this syndrome based on a support vector machine (SVM). METHODS: A family suffering from Deficiency-Cold syndrome is chosen for this study. This family has 5 patients with Deficiency-Cold syndrome and 10 normal members. The peripheral blood samples for these 5 patients and 5 normal members are tested by using cDNA microarray with 18,816 clones to get their differential expression genes. These genes are further explored to understand their biological functions and pathways through existing databases. A SVM model for clinical diagnosis is then developed based on these differential expression genes. RESULTS: A total of 83 differential expression genes were identified between patients and normal members, in which 21 genes were recorded in the FATIGO database and 16 genes were related to metabolism. Eight (8) pathways were sorted out in the KEGG database, and half pathways were associated with human metabolism. A discriminant mathematical model based on a support vector machine successfully predicted a normal person and a patient with heavy Deficiency-Cold syndrome based on their gene differential expression profiles. Thus, this model may classify the Deficiency-Cold syndrome. CONCLUSION: This work demonstrates that the differential expression genes can be used to identify normal persons and patients with Deficiency-Cold syndrome. Deficiency-Cold syndrome is mainly associated with the metabolism-related gene regulations. In addition, the discriminant mathematical model based on a support vector machine is applicable to the clinical diagnosis for Deficiency-Cold syndrome.

Adolescent↗