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At least 577 records · Page 32Linked to original sources
PubMed1984

Relation between intradental nerve activity and estimated pain in man--a mathematical model.

Intradental nerve activity (INA) induced by cold stimulation of human teeth is regularly accompanied by pain perception. In this study a mathematical model was developed in order to quantify the relationship between INA and pain. In 5 patients (45 experiments) INA was recorded using electrodes implanted in lower incisor teeth. Brief cold stimulations induced bursts of INA. The intensity of the resulting pain was simultaneously evaluated by means of an intermodal matching technique, finger span. The relationship between perceived pain and the integrated INA was analyzed using various mathematical operations (inter alia Fourier analysis) by means of a computer. A transfer function which describes the pain response following INA was found. This preliminary mathematical model, which is characterized by 5 parameters, consists of 2 parts, one which responds to fast changes in the afferent nerve signal, and another which reacts with a delay. The validity of the model has been tested, and it was found that the model consists of an adequate number of parameters and their cross-interaction is low. The analysis indicates that the parameters which determine the pain response following INA can be quantified and that they might be used as a measure of the efficacy of various pain relieving procedures.

Adult↗
PubMed2006

Mechanistic mathematical modelling of mercaptopurine effects on cell cycle of human acute lymphoblastic leukaemia cells.

The antimetabolite mercaptopurine (MP) is widely used to treat childhood acute lymphoblastic leukaemia (ALL). To study the dynamics of MP on the cell cycle, we incubated human T-cell leukaemia cell lines (Molt-4 sensitive and resistant subline and P12 resistant) with 10 microM MP and measured total cell count, cell cycle distribution, percent viable, percent apoptotic, and percent dead cells serially over 72 h. We developed a mathematical model of the cell cycle dynamics after treatment with MP and used it to show that the Molt-4 sensitive controls had a significantly higher rate of cells entering apoptosis (2.7-fold, P<0.00001) relative to the resistant cell lines. Additionally, when treated with MP, the sensitive cell line showed a significant increase in the rate at which cells enter apoptosis compared to its controls (2.4-fold, P<0.00001). Of note, the resistant cell lines had a higher rate of antimetabolite incorporation into the DNA of viable cells (>1.4-fold, P<0.01). Lastly, in contrast to the other cell lines, the Molt-4 resistant subline continued to cycle, though at a rate slower relative to its control, rather than proceed to apoptosis. This led to a larger S-phase block in the Molt-4 resistant cell line, but not a higher rate of cell death. Gene expression of apoptosis, cell cycle, and repair genes were consistent with mechanistic dynamics described by the model. In summary, the mathematical model provides a quantitative assessment to compare the cell cycle effects of MP in cells with varying degrees of MP resistance.

Antimetabolites, Antineoplastic↗
PubMed1988

The ability of a mathematical model to evaluate the effects of two pain modulating procedures on pulpal pain in man.

The ability of a mathematical model to evaluate the effects of two different pain modulating procedures (partial nerve block and vibration) on acute experimental pulpal pain was studied. The results were also compared with placebo procedures and it was shown that the model could accurately quantify the parameters that determine the pain response following cold-induced intradental nerve impulse activity (INA). The most effective pain relieving method was found to be partial nerve block which induced significant parameter alterations reflecting decreased pain sensation and increased reaction time. Thus, it was shown that the present mathematical model is a useful tool enabling detailed analysis of differences in pain relieving procedures on human pulpal pain mediated by nerves of the A type.

Adult↗
PubMed1991

A mathematical model relating response durations to amount of subclinical resistant disease.

A mathematical model is presented which seeks to determine, from examination of the response durations of a group of patients with malignant disease, the mean and distribution of the resistant tumor volume. The mean tumor-doubling time and distribution of doubling times are also estimated. The model assumes that in a group of patients there is a log-normal distribution both of resistant disease and of tumor-doubling times and implies that the shapes of certain parts of an actuarial response-duration curve are related to these two factors. The model has been applied to data from two reported acute leukemia trials: (a) a recent acute myelogenous leukemia trial was examined. Close fits were obtained for both the first and second remission-duration curves. The model results suggested that patients with long first remissions had less resistant disease and had tumors with slower growth rates following second line treatment; (b) an historical study of maintenance therapy for acute lymphoblastic leukemia was used to estimate the mean cell-kill (approximately 10(4) cells) achieved with single agent, 6-mercaptopurine. Application of the model may have clinical relevance, for example, in identifying groups of patients likely to benefit from further intensification of treatment.

Humans↗
PubMed1998

Field evaluation of a mathematical model of PCB transfer through the freshwater aquatic food chain.

A mathematical model of the transfer of PCBs through the freshwater aquatic food chain is described. The model predicts concentrations of 11 selected individual PCB congeners in forage fish and pike, from source terms of atmospheric deposition and watershed soil concentrations. Model performance has been evaluated using data from a field study conducted in a section of the River Severn near Birmingham, UK. Results demonstrate that with the exception of congener 52, overall model predictions of individual PCB concentrations in both forage fish and pike underestimate measured concentrations by factors of between approximately 3 and 25 for individual congeners. Closer examination suggests that whilst model equations contribute to these underestimations, a significant factor is the lack of knowledge of additional PCB inputs to the waterbody.

Animals↗
PubMedDate not supplied

Mathematical models to predict long bone lengths by transvaginal scan at 11-16 weeks' gestation.

OBJECTIVE: To propose a new mathematical model to estimate the length of fetal long bones in early pregnancy that can be used in the routine clinical setting. METHODS: In a group of 400 singleton normal fetuses, referred for transvaginal ultrasound examination between 11 and 16 weeks' gestation prior to genetic amniocentesis, a regression analysis was performed to evaluate the relationship between femur length (FLl) (mm) and biparietal diameter (BPD) (mm) and gestational age (GA) (days), as well as between humerus length (HL) (mm) and BPD (mm) and GA (days). The confidence intervals (CIs) of the predicted values for different values of BPD and for different gestational periods and CIs for the regression coefficients are stated as the mean +/- SD of standardized residuals. The accuracy of our best models obtained were evaluated at each gestational week between 11 and 16 with a 10% error cut-off limit. RESULTS: The best relationships between FL and HL versus BPD and GA are: expected FL = -16.92108 + 0.4569402 BPD +0.171617 GA (R(2) = 0.86) and expected HL = -16.28531 + 0.4283019 BPD + 0.1696017 GA (R(2) = 0.88), respectively. When a cut-off limit of 10% in estimating fetal long bones was utilized, the mathematical models revealed a good accuracy particularly at 13-14 weeks' gestation, a period when transvaginal biometric and morphologic examination is advisable and the highest percentage of scans are performed. DISCUSSION: Our proposed two linear models had a very good ability to estimate FL and HL and, due to the simplicity of the calculations, would be particularly useful in the routine clinical setting.

Bone Diseases↗
PubMed1969

Flow through a collapsible tube. Experimental analysis and mathematical model.

Flow through thin-wall axisymmetric tubes has long been of interest to physiologists. Analysis is complicated by the fact that such tubes will collapse when the transmural pressure (internal minus external pressure) is near zero. Because of the absence of any body of related knowledge in other sciences or engineering, previous workers have directed their efforts towards experimental studies of flow in collapsible tubes. More recently, some attention has been given towards analytical studies. Results of an extensive series of experiments show that the significant system parameter is transmural pressure. The cross-sectional area of the tube depends upon the transmural pressure, and changes in cross-section in turn affect the flow geometry. Based on experimental studies, a lumped parameter system model is proposed for the collapsible tube. The mathematical model is simulated on a hybrid computer. Experimental data were used to define the functional relationship between cross-sectional area and transmural pressure as well as the relation between the energy loss coefficient and cross-sectional area. Computer results confirm the validity of the model for both steady and transient flow conditions.

Computers, Hybrid↗
PubMed2000

A mathematical model for kinetic study of analyte permeation from both liquid and gas phases through hollow fiber membranes into vacuum

A mathematical model and a Matlab-5 computer code have been developed to study the dynamic response of the hollow fiber membrane probe. The depletion layer formation at the sample/membrane interface is taken into consideration by the mathematical model for the liquid mobile phase. The code produces concentration profiles within a sample feed stream and in the membrane. Flux values at the vacuum side of the membrane can also be calculated as a function of time. The method can be applied both for gas and liquid feed streams. Concentration profiles in a mobile phase and the flux of analytes through the hollow fiber membrane inlet have been studied with this simulation technique as a function of the liquid-phase flow rate. The influence of the formation of a layer of the analyte depletion during the dynamic response has been considered. The shape of the depleted layer and selectivity of permeation from a liquid mobile phase through the membrane into the vacuum are shown to be dependent on the mobile-phase flow rate. In addition, for studied conditions, formation of a depletion layer is demonstrated to be fast compared with membrane diffusion. Thus, if a homogeneous aqueous sample is coming through the inlet cross-section of a hollow fiber membrane containing pure water, the response time mostly depends on analyte diffusivity in the membrane. However, if the aqueous sample is coming through the inlet cross-section of a hollow fiber membrane containing clean air, response time also depends on equilibrium analyte concentration in the depletion layer.

Journal Article↗
PubMed1989

Incorporation of measured photosynthetic rate in a mathematical model for calculation of non-structural saccharide concentration.

A simple mathematical model for calculating the concentration of mobile carbon skeletons in the shoot of soya bean plants [Glycine max (L.) Merrill cv. Ransom] was built to examine the suitability of measured net photosynthetic rates (PN) for calculation of saccharide flux into the plant. The results suggest that either measurement of instantaneous PN overestimated saccharide influx or respiration rates utilized in the model were underestimated. If neither of these is the case, end-product inhibition of photosynthesis or waste respiration through the alternative pathway should be included in modelling of CH2O influx or efflux; and even if either of these is the case, the model output at a low coefficient of leaf activity indicates that PN still may be controlled by either end-product inhibition or alternative respiration.

Carbohydrate Metabolism↗
PubMed1981

Finite difference solution of a two-dimensional mathematical model of the cochlea.

A current, linear, two-dimensional mathematical model of the mechanics of the cochlea is solved numerically by using a finite difference approximation of the model equations. The finite-difference method is used to discretize Laplace's equation over a rectangular region with specified boundary conditions. The resulting matrix equation for fluid pressure is solved by using a Gaussian block-elimination technique. Numerical solutions are obtained for fluid pressure and basilar membrane displacement as a function of distance from the stapes. The finite difference method is a direct, versatile, and reasonably efficient means of solving the two-dimensional cochlear model.

Basilar Membrane↗
PubMed1992

A mathematical model of the mechanism of vertebrate somitic segmentation.

A mathematical model for the mechanism of periodic pattern formation in the process of somitogenesis is proposed. It is assumed that the metameric arrangement first appears before somite formation at the stage of transition of mesodermal cells into a polarized state. The model is based on the assumption that besides the mechanism of contact cell polarization there exists a mechanism of polarization suppression due to excretion of some chemical substance by polarized cells. Periodicity appears as a result of interaction of a kinematic wave of somitogenic cell determination with the cell cycles of mesodermal cells.

Animals↗
PubMed2003

An improved mathematical model of the ovulatory cycle of the laying hen.

1. The mathematical model of the hen's ovulatory cycle proposed by Etches and Schoch (British Poultry Science, 25: 65-76, 1984) predicts ovulation times for sequences of 2 to 9 ovulations only. 2. Continuous functions have been produced, representing the changes required to the parameters lambda1, lambda2, S1, S2, b1, b2 and b3, such that the prediction of any sequence length is now possible. 3. This improved ovulation model is capable of predicting ovulation times and intra-sequence ovulation intervals for any ovulation rate between 0.5 and 1.0. 4. The improved ovulatory model lends itself to stochasticity. The rate of lay of a population of hens at a time may be modelled with the use of means and standard errors for each of the parameters in the model. 5. Age-related changes in the ovulation rate of the population may be predicted using a combination of three methods, which are consistent with published theories that account for the decline in performance with time.

Animals↗
PubMed1982

Mathematical modelling of intravascular thyroid hormone stimulation by carrier proteins.

A simple mathematical model for the thyroid hormone stimulation in plasma after intravenous administration of pharmacological doses of thyroid hormone binding carrier proteins is described. The model concept is based on the observation of the time course of both radioactive labelled and unlabelled thyroid hormones before and after protein loading in rabbits. All model parameters are derived from experimental measurements in order to guarantee the identifiability with physiological data. The presented initial study could be a theoretical basis for a more effective therapy of thyroid storm by dialysis or plasma exchange methods.

Animals↗
PubMed1994

Mathematical model of TMA+ diffusion and prediction of light-dependent subretinal hydration in chick retina.

PURPOSE: To derive a mathematical model of TMA+ diffusion across the retina that can be used to estimate the amplitude and kinetics of the light-evoked increase in subretinal hydration and its effect on the concentration of other ions. METHODS: All experimental data were obtained in chick retina-pigment epithelium-choroid preparations as described in the accompanying paper. RESULTS: Diffusional properties of the retina were derived from the time course of [TMA+]o in the subretinal space (SRS) after changes in the retinal perfusate. Then, the SRS volume changes underlying the light-induced [TMA+]o response can be derived using a mathematical model of TMA+ diffusion. Complete retinal depth series of light-evoked [TMA+]o responses could be simulated by producing a corresponding expansion of the SRS. Volume changes inferred from the diffusion model were 2.2 to 3.8 times larger and more prolonged than could be derived directly from delta [TMA+]o. The model predicted up to a 20% peak increase in subretinal-space hydration during illumination. The effects of this volume increase on subretinal K+ and Ca2+ were estimated. These predictions were supported by inhibiting the volume increase with DIDS, which blocks retinal pigment epithelium basal membrane Cl- conductance. CONCLUSIONS: The primary source of light-evoked changes in extracellular TMA+ concentration recorded throughout the retina is an increase in hydration (volume) of the subretinal space. The response spreads to the inner retina by diffusion. Effects of TMA+ diffusion lead to large underestimates of the underlying volume changes. The light-evoked volume change alters the composition of the subretinal space and light-induced responses of other ions.

Animals↗
PubMed1979

Mathematical model for studying genetic variation in terms of restriction endonucleases.

A mathematical model for the evolutionary change of restriction sites in mitochondrial DNA is developed. Formulas based on this model are presented for estimating the number of nucleotide substitutions between two populations or species. To express the degree of polymorphism in a population at the nucleotide level, a measure called "nucleotide diversity" is proposed.

Base Sequence↗
PubMed1982

Mathematical modelling of cyclic AMP-Ca2+ interactions in pancreatic islets.

A mathematical model is proposed to account for the interactions between Ca2+ and cyclic AMP in the process of glucose-induced insulin release. This model allows simulation of experimental findings such as the glucose-induced accumulation of cyclic AMP in islet cells, the calcium dependency of the latter accumulation, the time course of 45Ca net uptake by the islets exposed to glucose and/or a phosphodiesterase inhibitor, the stimulation of insulin release by glucose, the suppression of such a release at low extracellular Ca2+ concentration and its amplification by phosphodiesterase inhibitors, the restoration of a significant secretory response to glucose in islets deprived of Ca2+ but exposed to a phosphodiesterase inhibitor, and the usual relationship between 45Ca net uptake and insulin release. All these data refer to studies performed over a 90-min incubation. The model is not suitable, however, to simulate the rapid response of the islet cells during the first few minutes that follow a change in the environment of the islets.

1-Methyl-3-isobutylxanthine↗
PubMedDate not supplied

[The mathematical modelling of the changes in energy metabolism in animal ontogeny].

A mathematical modeling of the intensity of respiration during growth is performed on the basis of equations that contain an intermediate independent variable tau. The model imitates k of peaks and lulls characteristic of the postembryonic period, which are followed by a continuous decrease in the energy level. The form of the equation for tau allowed us to suggest a hypothesis dealing with interactions of k + 1 cell generations, each bearing an imprinting of corresponding stage of development.

Animals↗
PubMed1994

Mathematical model application to the kinetic study of tumor markers.

In order to overcome the inefficient cutoff criterion in the management of neoplastic patients after therapy, in follow-up, in recurrence and in monitoring treatment, we have analysed some mathematical models to evaluate serial determinations of tumor markers, with the aim to ascertain the radicality of surgery or the presence of recurrences. Since a tracer study of the biological system of tumor markers is impossible, some information, such as rate factor and half-life, is obtained by determination of the marker after radical treatment. In steady state with two or more samples in time it is possible with adequate statistical models to establish a significant increase in the marker. In recurrence, if it is true that the secretion rate of the marker by a tumor is proportional to tumor mass, then increasing concentrations of the tumor marker would be a phenotypic expression of tumor growth. Therefore some mathematical models are proposed to evaluate the kinetics of tumor growth.

Biomarkers, Tumor↗