Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “MATHEMATICS”

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 235 records · Page 13Linked to original sources
PubMed2001

Cytocidal effect and DNA damage of nedaplatin: a mathematical model and analysis of experimental data.

PURPOSE: Cell cycle non-specific anticancer agents such as cis-diamminedichloroplatinum(II) are believed to depend linearly on the value of the area under the drug concentration time curve, which is supported by a mathematical model. However, the quantitative non-linear phenomena of both the cytocidal effect and DNA crosslink formation by cisdiammine(glycolato)platinum (nedaplatin) have been shown in vitro. Therefore, we developed a new mathematical model to explain these phenomena. METHODS: We assumed that nedaplatin enters intracellular fluid from medium through simple diffusion to form DNA crosslinks that kill cells. We developed a mathematical model to represent this assumption using differential equations that we then solved using an original computer program. The calculated results were compared with the experimental data. RESULTS: The drug's simple diffusion rate constant, the DNA crosslink formation rate constant, and the crosslink-dependent cell death rate constant in the model were 1.8 x 10(-14) (l h-1), 1.6 x 10(8) (l mol-1/2 h-1), 5.45 x 10(1) (mol-1), respectively. The model fits the experimental results statistically. The model also demonstrated theoretical proof that continuous exposure at a low dose was superior to the short exposure at a high dose seen in published experimental data. CONCLUSIONS: We developed a mathematical model to describe the non-linear pharmacodynamic effect of nedaplatin in vitro. This model may provide a novel drug infusion procedure for cancer patients.

Antineoplastic Agents↗
PubMed2001

The diffusive transport of gibberellins and abscisic acid through the aleurone layer of germinating barley grain: a mathematical model.

A mathematical model of the diffusive transport of abscisic acid (ABA) and gibberellins (GAs) through the aleurone layer of barley (Hordeum vulgare L.) grain is presented. The model consists of two partial differential equations describing the accumulation of phytohormone in the apoplastic and symplasmic compartments of the aleurone layer, both spatially and temporally. The mathematical model contains the morphology of the barley grain and the physicochemical properties of the two phytohormones. A mathematical derivation of the accumulation ratios for the two phytohormones between the symplast and apoplast under equilibrium conditions resulted in different distribution mechanisms for GAs and ABA. A sensitivity analysis of the accumulation ratio for GAs indicated high sensitivity to the apoplastic pH and the membrane potential, whereas the accumulation ratio for ABA proved to be most sensitive to the pH difference between the apoplast and symplast. The diffusive transport time for GAs to the basal site of the aleurone layer as calculated with the mathematical model is within a physiologically plausible timescale according to experimental data from the literature. Abscisic acid cannot be transported by diffusion to the end of the aleurone layer as quickly as GAs, according to model simulations. Therefore, the functional role of ABA in germination is likely to be in the vicinity of the embryo.

Abscisic Acid↗
PubMed2006

Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results.

The combined use of experimental and mathematical models can lead to a better understanding of fracture healing. In this study, a mathematical model, which was originally established by Bailón-Plaza and van der Meulen (J Theor Biol 212:191-209, 2001), was applied to an experimental model of a semi-stabilized murine tibial fracture. The mathematical model was implemented in a custom finite volumes code, specialized in dealing with the model's requirements of mass conservation and non-negativity of the variables. A qualitative agreement between the experimentally measured and numerically simulated evolution in the cartilage and bone content was observed. Additionally, an extensive parametric study was conducted to assess the influence of the model parameters on the simulation outcome. Finally, a case of pathological fracture healing and its treatment by administration of growth factors was modeled to demonstrate the potential therapeutic value of this mathematical model.

Animals↗
PubMed1991

Forecasting the number of future disabled elderly using Markovian and mathematical models.

The accuracy of forecasting the number of future disabled elderly people depends on the accuracy of projecting mortality rates and the rates of transition to and from functional disability. We describe a new two-step method for constructing mathematical models that project these future rates dynamically. (1) A Markovian model of elders' transitions between functional states is specified. (2) A mathematical model of the probability of each transition is created. We conducted pilot studies of the fundamental mathematical processes of this method using data from the Longitudinal Study of Aging. First we constructed prototypic mathematical models of the probabilities of remaining functionally able and of making transitions to disability and to death within 2 years. Then we used these models to project hypothetical rates of transition for white women of selected ages, morbidity ratings and health statuses.

Activities of Daily Living↗
PubMed2006

Local controlled drug delivery to the brain: mathematical modeling of the underlying mass transport mechanisms.

The mass transport mechanisms involved in the controlled delivery of drugs to living brain tissue are complex and yet not fully understood. Often the drug is embedded within a polymeric or lipidic matrix, which is directly administered into the brain tissue, that is, intracranially. Different types of systems, including microparticles and disc- or rod-shaped implants are used to control the release rate and, thus, to optimize the drug concentrations at the site of action in the brain over prolonged periods of time. Most of these dosage forms are biodegradable to avoid the need for the removal of empty remnants after drug exhaustion. Various physical and chemical processes are involved in the control of drug release from these systems, including water penetration, drug dissolution, degradation of the matrix and drug diffusion. Once the drug has been released from the delivery system, it has to be transported through the living brain tissue to the target site(s). Again, a variety of phenomena, including diffusion, drug metabolism and degradation, passive or active uptake into CNS tissue and convection can be of importance for the fate of the drug. An overview is given of the current knowledge of the nature of barriers to free access of drug to tumour sites within the brain and the state of the art of: (i) mathematical modeling approaches describing the physical transport processes and chemical reactions which can occur in different types of intracranially administered drug delivery systems, and of (ii) theories quantifying the mass transport phenomena occurring after drug release in the living tissue. Both, simplified as well as complex mathematical models are presented and their major advantages and shortcomings discussed. Interestingly, there is a significant lack of mechanistically realistic, comprehensive theories describing both parts in detail, namely, drug transport in the dosage form and in the living brain tissue. High quality experimental data on drug concentrations in the brain tissue are difficult to obtain, hence this is itself an issue in testing mathematical approaches. As a future perspective, the potential benefits and limitations of these mathematical theories aiming to facilitate the design of advanced intracranial drug delivery systems and to improve the efficiency of the respective pharmacotherapies are discussed.

Animals↗
PubMed2007

Mathematical modeling as a tool for investigating cell cycle control networks.

Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.

Animals↗
PubMed2001

Application of a new mathematical function for describing chromatographic peaks.

Curve fitting seems to be one of the best methods for the evaluation of chromatographic signals. As it is known, in this case mathematical function is fitted to digitized measured points. The most important task is to find the best mathematical function, which corresponds perfectly to the peak shape, and then to determine the parameters of the equation using a computerized least-squares method of approximation. In this work, a new mathematical function was sought for with the purpose of describing different chromatographic signals and it was fitted to the digitized measured points. The fitted curve is suitable for a quick evaluation of chromatographic information, noise filtering and correction of baseline drift. The fitting of gas chromatographic and high-performance liquid chromatographic signals were completed. The mathematical function, the generated chromatographic curves, the application of the function for describing real signals and the fitting process will be demonstrated in this study.

Chromatography, Gas↗
PubMed2003

The dynamics of T-cell fratricide: application of a robust approach to mathematical modelling in immunology.

Fratricide between CD8(+) T lymphocytes is known to occur in HTLV-I and possibly HSV-1 and HIV-1 infection. However it is not known what effect, if any, T-cell fratricide has on the course of infection. Here we present simple mathematical techniques to investigate T-cell fratricide with particular reference to HTLV-I infection. Using a general model we predict the qualitative and quantitative effect of fratricide on HTLV-I equilibrium proviral load. We also investigate the effect of fratricide on the probability of viral clearance. We show that, surprisingly, fratricide can lead either to an increase or a decrease in equilibrium proviral load. We derive the conditions necessary for fratricide to cause a decrease in load and deduce that, for the five HTLV-I-positive patients considered here, fratricide has probably caused an increase in equilibrium load. We also estimate the percentage increase in load that is attributable to fratricide and determine the parameters that should be measured in order to improve this estimate. Finally, we show that fratricide reduces the probability of viral clearance. Mathematical modelling of HTLV-I infection, as is often the case in biology, is severely hampered by a lack of experimental data. Consequently it is difficult to know what functional form a model should take. The behaviour of complex nonlinear systems is highly model-dependent. Predictions based on theoretical models are therefore sensitive to the choice of model; this is a very severe problem that undermines and limits the success of the application of mathematics to immunology. In this paper we reduce the model dependency of the results in two ways-by considering (analytically) a general model with a minimal number of assumptions and, where this is not possible, by checking (numerically) that a wide range of models yield the same results. We therefore begin to develop two practical methods for dealing with the problem of robustness in mathematical models of the immune system.

CD8-Positive T-Lymphocytes↗
PubMedDate not supplied

Mathematical modelling and quantitative methods.

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

Animals↗
PubMed2004

A mathematical model for prediction of drug molecule diffusion across the blood-brain barrier.

BACKGROUND: Predicting the ability of drugs to enter the brain is a longstanding problem in neuropharmacology. The first step in creating a much-needed computational algorithm for predicting whether a drug will enter brain is to devise a rigorous mathematical model. METHODS: Employing two experimental measures of blood-brain barrier (BBB) penetrability (brain/plasma ratio and the brain-uptake index) and 14 theoretically derived biophysical predictors, a mathematical model was developed to quantitatively correlate molecular structure with ability to traverse the BBB. RESULTS: This mathematical model employs Stein's hydrogen bonding number and Randic's topological descriptors to correlate structure with ability to cross the BBB. The final model accurately predicts the ability of test molecules to cross the BBB. CONCLUSIONS: A mathematical method to predict blood-brain barrier penetrability of drug molecules has been successfully devised. As a result of bioinformatics, chemoinformatics and other informatics-based technologies, the number of small molecules being developed as potential therapeutics is increasing exponentially. A biophysically rigorous method to predict BBB penetrability will be a much-needed tool for the evaluation of these molecules.

Algorithms↗
PubMed2002

An intervention program for promoting deaf pupils' achievement in mathematics.

Our past research identified two aspects of deaf children's functioning that places them at risk for underachievement in mathematics. The first is their reduced opportunities for incidental learning, and the second is their difficulty in making inferences involving time sequences. This article examines the effectiveness of an intervention program to promote deaf children's numeracy that was designed to deal with these two factors. The design involved a comparison of 23 deaf pupils participating in the project with a baseline group formed by 65 deaf pupils attending the same schools in the previous year. The project pupils were tested before and after the intervention on the NFER-Nelson Age Appropriate Mathematics Achievement Test. The intervention was delivered by the teachers during the time normally scheduled for mathematics lessons. The project pupils did not differ from the baseline group at pretest but performed significantly better at posttest. They also performed at posttest better than expected on the basis of their pretest scores, according to norms provided by the NFER-Nelson Age Appropriate Mathematics Test for assessing the progress of hearing pupils. We conclude that the program was effective in promoting deaf pupils' achievement in numeracy.

Journal Article↗
PubMed2005

Mathematical models for pressure controlled ventilation of oleic acid-injured pigs.

One-compartment, mathematical models for pressure controlled ventilation, incorporating volume dependent compliances, linear and nonlinear resistances, are constructed and compared with data obtained from healthy and (oleic acid) lung-injured pigs. Experimental data are used to find parameters in the mathematical models and were collected in two forms. Firstly, the P(e)-V curves for healthy and lung injured pigs were constructed; these data are used to compute compliance functions for each animal. Secondly, dynamic data from pressure controlled ventilation for a variety of applied pressures are used to estimate resistance parameters in the models. The models were then compared against the collected dynamic data. The best mathematical models are ones with compliance functions of the form C(V) = a + bV where a and b are constants obtained from the P(e)-V curves and the resistive pressures during inspiration change from a linear relation P(r) = RQ to a nonlinear relation P(r) = RQ(epsilon) where Q is the flow into the one-compartment lung and epsilon is a positive number. The form of the resistance terms in the mathematical models indicate the possible presence of gas-liquid foams in the experimental data.

Animals↗
PubMed2002

A mathematical model of cell salvage efficiency.

UNLABELLED: Cell salvage (CS) is one of the modalities that can be used during surgery to decrease the use of allogeneic blood. Unlike acute normovolemic hemodilution, the efficiency of CS has not been mathematically modeled. In this article, we hypothesized that a mathematical model could predict the decline of hematocrit during CS. The model that was developed accounts for both the effect of decreasing the hematocrit because of blood loss and the effect of increasing hematocrit because of the readministration of washed blood in an isovolemic patient. The efficiency of CS is defined to be the maximum allowable blood loss (MABL) for a fixed blood volume and a fixed transfusion trigger. For demonstration purposes, variables used for a hypothetical patient included an estimated blood volume of 5000 mL, a presurgery hematocrit of 45%, and a transfusion trigger of 21%. The MABL in a typical case was 9600 mL, with a CS red cell recovery rate of 60%. Patient records from a convenience sample showed an average recovery rate of 57% with 20% variability. This mathematical model suggests that CS can be a highly effective blood conservation method when red blood cell collection is optimal. IMPLICATIONS: In this study, a mathematical model of cell salvage was developed. The model was then matched against real clinical cases to gain an understanding of the variables that modify cell salvage efficiency. The model illustrates that cell salvage can be a highly effective method of avoiding blood transfusion.

Algorithms↗
PubMed2004

Mathematical models of the embryo and fetus for use in radiological protection.

This development of new mathematical models arose from our current work in external neutron dosimetry for the embryo and fetus when pregnant women travel at commercial aircraft altitudes. A problem of concern in radiation protection is exposure of pregnant women to ionizing radiation because of the high radiosensitivity of the embryo and fetus. Special regulations and dosimetric considerations are necessary for pregnant women at the work place and in the public. To perform dosimetry, mathematical models for the embryo and the fetus, together with the modified adult female model for pregnant woman, are required. There are no models available for embryo. Models developed for the fetus need to be updated with the new reference values such as those in ICRP Publication 89. This article presents mathematical models for the embryo and fetus at different stages: the embryo at 8 wk and the fetus at the end of each trimester. In addition to fetal skeleton, the fetal brain is explicitly modeled because of its high radiosensitivity. All model parameters are determined from the most recent reference values available. The models are designed so that an interpolation can be easily performed to generate a model of embryo/fetus at any given stage of development. This feature also allows convenient adaptation of the models to different reference values representing various ethnic populations. The new mathematical models presented here were developed for external dosimetry. They can also be used for internal dosimetry purposes, if other organs inside the female phantom are adjusted accordingly.

Adult↗
PubMed1989

Interactive, mathematical, and sequential consultative methods in diagnosing renal masses on excretory urograms.

Using the clinical setting of diagnosing renal masses on excretory urograms, we compared the diagnostic efficacy and costs resulting from different consultative methods. These included face-to-face interactive consultation, mathematical combination of a fixed number of radiologists' confidence judgments, and computerized sequential decision making. This last method mathematically combines a variable number of individual judgments into an aggregate diagnosis based on diagnostic certainty. Six radiologists interpreted 42 proven urograms individually, with face-to-face consultation for selected cases, and interactively in groups of three. Individual diagnostic probability estimations were mathematically combined for the mathematical and sequential models. All models of consultation resulted in both higher diagnostic accuracy and lower costs than individual radiologists interpreting urograms alone. While the sequential model provided the highest diagnostic efficacy, it was only slightly more accurate than the other models tested. Radiologists interactively consulting on cases they considered difficult was the least costly method, approximating the projected costs of sequential decision making. Interactive consultation among radiologists is a cost-effective practice; sequential decision-making is a promising technique for improving diagnostic efficacy and reducing costs, and further evaluation is warranted.

Carcinoma, Renal Cell↗
PubMed2003

An introduction to lymphocyte and viral dynamics: the power and limitations of mathematical analysis.

Mathematics is a useful tool in the analysis and understanding of population dynamic aspects of the immune response. However, the power of mathematical modelling in immunology is frequently limited by the shortage of experimental data. Here, we review the contribution of mathematics to two areas of immunology. We highlight the problem caused by lack of knowledge of the system, which can greatly restrict the use of mathematics and lead to errors caused by model-specific results.

Lymphocytes↗
PubMed1992

Mathematical modeling and spectrum analysis of the physiological patello-femoral pulse train produced by slow knee movement.

Analysis of vibration signals emitted by the knee joint has the potential for the development of a noninvasive procedure for the diagnosis and monitoring of knee pathology. In order to obtain as much information as possible from the power density spectrum of the knee vibration signal, it is necessary to identify the physiological factors (or physiologically relevant parameters) that shape the spectrum. This paper presents a mathematical model for knee vibration signals, in particular the physiological patello-femoral pulse (PFP) train produced by slow knee movement. It demonstrates through the mathematical model that the repetition rate of the physiological PFP train introduces repeated peaks in the power spectrum, and that it affects the spectrum mainly at low frequencies. The theoretical results also show that the spectral peaks at multiples of the PFP repetition rate become more evident when the variance of the interpulse interval (IPI) is small, and that these spectral peaks shift toward higher frequencies with increasing PFP repetition rates. To evaluate the mathematical model, a simulation algorithm was developed, which generates PFP signals with adjustable repetition rate and IPI variance. Signals generated by simulation were seen to possess representative spectral characteristics typically observed in physiological PFP signals. This simulation procedure allows an interactive examination of several factors which affect the PFP train spectrum. Finally, in vivo measurements of physiological PFP signals of normal volunteers are presented. Results of simulations and analysis of signals recorded from human subjects support the mathematical model's prediction that the IPI statistics play a very significant role in determining the low-end power spectrum of the physiological PFP signal.(ABSTRACT TRUNCATED AT 250 WORDS)

Algorithms↗
PubMed1993

Mathematical modeling of ligaments and tendons.

Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model.

Animals↗