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 433 records · Page 24Linked to original sources
PubMed2001

Mathematical analysis of frontal affinity chromatography in particle and membrane configurations.

The scaleup and optimization of large-scale affinity-chromatographic operations in the recovery, separation and purification of biochemical components is of major industrial importance. The development of mathematical models to describe affinity-chromatographic processes, and the use of these models in computer programs to predict column performance is an engineering approach that can help to attain these bioprocess engineering tasks successfully. Most affinity-chromatographic separations are operated in the frontal mode, using fixed-bed columns. Purely diffusive and perfusion particles and membrane-based affinity chromatography are among the main commercially available technologies for these separations. For a particular application, a basic understanding of the main similarities and differences between particle and membrane frontal affinity chromatography and how these characteristics are reflected in the transport models is of fundamental relevance. This review presents the basic theoretical considerations used in the development of particle and membrane affinity chromatography models that can be applied in the design and operation of large-scale affinity separations in fixed-bed columns. A transport model for column affinity chromatography that considers column dispersion, particle internal convection, external film resistance, finite kinetic rate, plus macropore and micropore resistances is analyzed as a framework for exploring further the mathematical analysis. Such models provide a general realistic description of almost all practical systems. Specific mathematical models that take into account geometric considerations and transport effects have been developed for both particle and membrane affinity chromatography systems. Some of the most common simplified models, based on linear driving-force (LDF) and equilibrium assumptions, are emphasized. Analytical solutions of the corresponding simplified dimensionless affinity models are presented. Particular methods for estimating the parameters that characterize the mass-transfer and adsorption mechanisms in affinity systems are described.

Chromatography, Affinity↗
PubMed2001

Neural network analysis in predicting 2-year survival in elderly people: a new statistical-mathematical approach.

We designed this study to test the usefulness of artificial neural networks (ANN) in assessing 2-year survival in elderly persons, and to understand the net's logical functioning, thus determining the relative importance of the single biological and clinical variables which influence survival. ANN are statistical-mathematical tools able to determine the existence of a correlation between series of data and, once 'trained', to predict output data given input data. Although ANN have been applied in various areas of medical research, they have only very recently been applied in geriatrics (Cacciafesta et al., 2000. Arch. Gerontol. Geriatr. 31 (in press)). We built up an ANN to investigate how 17 clinical variables relating to a sample of 159 elderly people affect survival, and the possibility of predicting 2-year survival or non-survival for each single subject. When tested on a sample of 20 elderly people, the trained network gave the correct answer in 85% of the cases. We then extracted the mathematical function that the net used for calculating the output (survival) for each set of input data (clinical variables). Using this formula, we investigated how some clinical variables influence 2-year survival: we found that a low serum cholesterol level is an unfavourable characteristic in relation to survival. We conclude-despite the fact that the sample studied was relatively small-that ANN are useful in predicting 2-year survival in elderly people. The mathematical function we obtained from the net seems useful in determining the relative importance of single variables related to survival.

Journal Article↗
PubMed2000

Inhibition-based rhythms: experimental and mathematical observations on network dynamics.

An increasingly large body of data exists which demonstrates that oscillations of frequency 12-80 Hz are a consequence of, or are inextricably linked to, the behaviour of inhibitory interneurons in the central nervous system. This frequency range covers the EEG bands beta 1 (12-20 Hz), beta 2 (20-30 Hz) and gamma (30-80 Hz). The pharmacological profile of both spontaneous and sensory-evoked EEG potentials reveals a very strong influence on these rhythms by drugs which have direct effects on GABA(A) receptor-mediated synaptic transmission (general anaesthetics, sedative/hypnotics) or indirect effects on inhibitory neuronal function (opiates, ketamine). In addition, a number of experimental models of, in particular, gamma-frequency oscillations, have revealed both common denominators for oscillation generation and function, and subtle differences in network dynamics between the different frequency ranges. Powerful computer and mathematical modelling techniques based around both clinical and experimental observations have recently provided invaluable insight into the behaviour of large networks of interconnected neurons. In particular, the mechanistic profile of oscillations generated as an emergent property of such networks, and the mathematical derivation of this complex phenomenon have much to contribute to our understanding of how and why neurons oscillate. This review will provide the reader with a brief outline of the basic properties of inhibition-based oscillations in the CNS by combining research from laboratory models, large-scale neuronal network simulations, and mathematical analysis.

Electroencephalography↗
PubMed2001

Mathematical modeling of bioerodible, polymeric drug delivery systems.

The aim of this article is to give an introduction into mathematical modeling approaches of bioerodible controlled drug delivery systems and to present the most important erosion theories reported in the literature. First, important parameters such as degradation and erosion are defined and physicochemical methods for their investigation are briefly presented. Then, phenomenological empirical models as well as models based on diffusion and chemical reaction theory are discussed. Due to the significant chemical and physicochemical differences among individual bioerodible polymers used for controlled drug delivery systems, various mathematical models have been developed to describe the chemical reactions and physical mass transport processes involved in erosion-controlled drug release. Various examples of practical applications of these models to experimental drug release data are given. For those involved in the design and development of biodegradable drug delivery systems this will help to choose the appropriate mathematical model for a specific drug release problem. Important selection criteria such as the desired predictive power and precision, but also the effort required to apply a model to a particular system will be discussed. Furthermore, before models can be used for drug release predictions certain parameters such as drug dissolution or polymer degradation rate constants, have to be known. The number of parameters to be determined significantly differs between the models. The practical benefit of carefully choosing the right model is that effects of composition and device geometry on the drug release kinetics can be predicted which can reduce laborious formulation studies to a minimum.

Drug Delivery Systems↗
PubMed2003

Mathematical modeling relevant to closed artificial ecosystems.

The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space.

Animals↗
PubMed2002

PLGA-based microparticles: elucidation of mechanisms and a new, simple mathematical model quantifying drug release.

The two major aims of this study were: (i) to elucidate the underlying release mechanisms from drug-loaded, erodible microparticles based on poly(lactic-co-glycolic acid) (PLGA) showing biphasic drug release behavior: an initial 'burst' effect, followed by a zero order release phase; and (ii) to develop a new, simple mathematical model that allows the quantitative description of the observed in vitro drug release patterns from this type of delivery system. PLGA-based microparticles offer various advantages, such as the possibility to control the resulting drug release rate accurately over prolonged periods of time, easiness of administration (e.g., by stereotaxic injection), good biocompatibility and complete erosion (avoiding the removal of empty remnants). Consequently, the practical importance of these advanced drug delivery systems is remarkably increasing. However, only little knowledge is yet available concerning the processes controlling the release rate of the drug out of these devices. Various chemical and physical phenomena are involved, rendering the identification of the crucial mechanisms and the mathematical description of the resulting drug release kinetics difficult. In the present study, different physicochemical characterization methods (e.g., DSC, SEM, SEC, particle size analysis) were used to monitor the changes occurring within anticancer drug-loaded PLGA microparticles upon exposure to phosphate buffer pH 7.4. Based on these experimental findings, the most important underlying drug release rate controlling mechanisms were identified and a new mathematical model was developed that allows the quantitative description of the resulting release patterns.

Buffers↗
PubMed2002

Archimedes: a new model for simulating health care systems--the mathematical formulation.

This paper designs an object-oriented, continuous-time, full simulation model for addressing a wide range of clinical, procedural, administrative, and financial decisions in health care at a high level of biological, clinical, and administrative detail. The full model has two main parts, which with some simplification can be designated "physiology models" and "models of care processes." The models of care processes, although highly detailed, are mathematically straightforward. However, the mathematics that describes human biology, diseases, and the effects of interventions are more difficult. This paper describes the mathematical formulation and methods for deriving equations, for a variety of different sources of data. Although Archimedes was originally designed for health care applications, the formulation, and equations are general and can be applied to many natural systems.

Computational Biology↗
PubMed2004

Concerted regulation of all hyphal tips generates fungal fruit body structures: experiments with computer visualizations produced by a new mathematical model of hyphal growth.

Filamentous hyphal growth is inherently suited to kinetic analysis, and in many respects the fungal mycelium can be viewed as a very mechanical biological system, which lends itself to mathematical modelling. The mathematics of hyphal tip extension growth are well-established. However, even though a hyphal growth equation can be written with confidence, and we have a good understanding of the effects of tropisms on growth, it is not easy to form a mental picture of the behaviour of large populations of hyphal tips. What is required, and what we believe we have produced, is a mathematical model that is sufficiently sophisticated to produce a realistic visualization of fungal hyphal growth. This provides us with a cyberfungus that can be used for experimentation on the theoretical rules that might govern hyphal patterning, hyphal interactions, and tissue formation and organ development by actually visualizing the virtual hyphal growth patterns that result from different regulatory scenarios. From a series of model experiments the most significant observation is that complex fungal fruit body shapes can be simulated by applying the same regulatory functions to all of the growth points active in a structure at any specific time. No global control of fruit body geometry is necessary. No localized regulation is necessary. The shape of the fruit body emerges from the concerted response of the entire population of hyphal tips, in the same way, to the same signals.

Computer Graphics↗
PubMedDate not supplied

Development of a transient segregated mathematical model of the semicontinuous microbial production process of dihydroxyacetone.

For the mathematical description of the semicontinuous two-stage repeated-fed-batch fermentation of dihydroxyacetone (DHA), a novel segregated model incorporating transient growth rates was developed. The fermentation process was carried out in two stages. A viable, not irreversibly product-inhibited culture was maintained in the first reactor stage until a predetermined DHA threshold value was reached. In the second reactor stage, high final product concentrations of up to 220 g L(-1) were reached while the culture was irreversibly product-inhibited. The experimentally observed changes of the physiological state of the culture due to product inhibition were taken into account by introducing a segregation into the mathematical model. It was shown that the state of the cells was dependent on the current environment and on the previous history. This phenomenon was considered in the model by utilizing delay time equations for the specific rates of growth on the primary and the secondary substrate. A comparison with reproducible measurements gave a good correlation between computation and experiment. The mathematical model was validated using independent own experimental data. A comparison with a stationary and nonsegregated model demonstrated the essential improvements of the novel model. It was deduced from the model calculations that high product formation rates of 3.3-3.5 g L(-1) h(-1) as well as high final DHA concentrations of 196-215 g L(-1) can be obtained with a residual broth volume in the first reactor stage of 2% and a DHA threshold value in the range of 100-110 g L(-1).

Bioreactors↗
PubMedDate not supplied

Mathematical modelling of angiogenesis.

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network. Subsequent cell proliferation near the sprout-tips permits further extension of the capillaries and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this article we first of all present a review of a variety of mathematical models which have been used to describe the formation of capillary networks and then focus on a specific recent model which uses novel mathematical modelling techniques to generate both two- and three-dimensional vascular structures. The modelling focusses on key events of angiogenesis such as the migratory response of endothelial cells to exogenous cytokines (tumour angiogenic factors, TAF) secreted by a solid tumour; endothelial cell proliferation; endothelial cell interactions with extracellular matrix macromolecules such as fibronectin; capillary sprout branching and anastomosis. Numerical simulations of the model, using parameter values based on experimental data, are presented and the theoretical structures generated by the model are compared with the morphology of actual capillary networks observed in in vivo experiments. A final conclusions section discusses the use of the mathematical model as a possible angiogenesis assay.

Animals↗
PubMed2002

Mathematical models of the balance between apoptosis and proliferation.

As our understanding of cellular behaviour grows, and we identify more and more genes involved in the control of such basic processes as cell division and programmed cell death, it becomes increasingly difficult to integrate such detailed knowledge into a meaningful whole. This is an area where mathematical modelling can complement experimental approaches, and even simple mathematical models can yield useful biological insights. This review presents examples of this in the context of understanding the combined effects of different levels of cell death and cell division in a number of biological systems including tumour growth, the homeostasis of immune memory and pre-implantation embryo development. The models we describe, although simplistic, yield insight into several phenomena that are difficult to understand using a purely experimental approach. This includes the different roles played by the apoptosis of stem cells and differentiated cells in determining whether or not a tumour can grow; the way in which a density dependent rate of apoptosis (for instance mediated by cell-cell contact or cytokine signalling) can lead to homeostasis; and the effect of stochastic fluctuations when the number of cells involved is small. We also highlight how models can maximize the amount of information that can be extracted from limited experimental data. The review concludes by summarizing the various mathematical frameworks that can be used to develop new models and the type of biological information that is required to do this.

Apoptosis↗
PubMed2002

A new mathematical model quantifying drug release from bioerodible microparticles using Monte Carlo simulations.

PURPOSE: The major objectives of this study were to 1) develop a new mathematical model describing all phases of drug release from bioerodible microparticles; 2) evaluate the validity of the theory with experimental data; and 3) use the model to elucidate the release mechanisms in poly(lactide-co-glycolide acid)-based microspheres. METHODS; 5-Fluorouracil-loaded microparticles were prepared with an oil-in-water solvent extraction technique and characterized in vitro. Monte Carlo simulations and sets of partial differential equations were used to describe the occurring chemical reactions and physical mass transport phenomena during drug release. RESULTS: The new mathematical model considers drug dissolution, diffusion with nonconstant diffusivities and moving boundary conditions, polymer degradation/erosion, time-dependent system porosities, and the three-dimensional geometry of the devices. In contrast with previous theories, this model is able to describe the observed drug release kinetics accurately over the entire period of time, including 1) initial "burst" effects; 2) subsequent, approximately zero-order drug release phases; and 3) second rapid drug release phases. Important information, such as the evolution of the drug concentration profiles within the microparticles, can be calculated. CONCLUSIONS; A new, mechanistic mathematical model was developed that allows further insight into the release mechanisms in bioerodible microparticles.

Biotransformation↗
PubMed1999

A mathematical model predicting anti-hepatitis B virus surface antigen (HBs) decay after vaccination against hepatitis B.

The determination of serum levels of antibodies against hepatitis B virus surface antigen (anti-HBs) after hepatitis B vaccination is currently the only simple test available to predict the decay of protection and to plan the administration of booster doses. A total of 3085 vaccine recipients of plasma-derived and recombinant vaccine have been followed for 10 years to determine the kinetics of anti-HBs production and to construct a mathematical model which could efficiently predict the anti-HBs level decline. The anti-HBs peak level was reached 68 days after the last dose of recombinant vaccine and 138 days after the last dose of plasma-derived vaccines. The age of vaccinees negatively influenced the anti-HBs levels and also the time necessary to reach the anti-HBs peak. A bilogarithmic mathematical model (log10 level, log10 time) of anti-HBs decay has been constructed on a sample of recombinant vaccine recipients and subsequently validated on different samples of recombinant or plasma-derived vaccine recipients. Age, gender, type of vaccine (recombinant or plasma-derived), number of vaccine doses (three or four) did not influence the mathematical model of antibody decay. The program can be downloaded at the site: http:@www2.stat.unibo.it/palareti/vaccine.htm . Introducing an anti-HBs determination obtained after the peak, the program calculates a prediction of individual anti-HBs decline and allows planning of an efficient booster policy.

Algorithms↗
PubMedDate not supplied

Understanding mathematical models for breast cancer risk assessment and counseling.

Chemoprevention and prophylactic surgery are effective interventions for lowering breast cancer incidence. However, these approaches are associated with risks of their own. Accurate individualized breast cancer risk assessment is an essential component of the risk/benefit analysis that must take place prior to implementing either of these strategies. Several mathematical models for estimating individual breast cancer risk have been proposed over the last decade. The Gail model is the most generally applicable model; however, it neglects family history information in second-degree relatives, treats pre- and postmenopausal breast cancer the same, and ignores personal histories of lobular neoplasia. The Claus model is a better family history model, but it does not assign any special relevance to histories of bilateral breast cancer or ovarian cancer, and neglects all of the nonfamily history information accounted for by the Gail model. BRCAPRO is a Bayesian family history model that calculates individual breast cancer probabilities based on the probability that a family carries a mutation in one of the BRCA genes. Though its treatment of family history information is more thorough than the other models, it neglects the nonfamily history risk factors accounted for by the Gail model and may not appreciate familial clustering unrelated to BRCA gene mutation. A thorough understanding of the principles of risk analysis and the available mathematical models is essential for anyone wishing to perform intervention counseling. This review describes the basic components of risk analysis, explains how the mathematical models work and compares the strengths and weaknesses of the various models. CancerGene is a software tool for running all of these models. It may be obtained without charge at http://www.swmed.edu/home_pages/cancergene.

Breast Neoplasms↗
PubMed1991

[Effect of a mathematical model and number of measurements on accuracy in fetal weight estimation using ultrasound].

The problem of foetal weight estimation has not been satisfactorily solved to date. We studied quantitatively the influence of the mathematical approach and the number of distance measurements of different parts of the foetal body, on the accuracy of prospective calculation of the actual foetal weight. Of 230 foetuses of known gestational age we measured via ultrasound 13 lengths of head, rump and extremities during the last three days before delivery. 22 types of formulas were analysed. To decide on the best mathematical way of calculation we recalculated all coefficients in all formulas for each study group. In this way each formula can yield best possible results for the presented group. Three formulas yield very good results--a logarithmic type using 7 measured distances, and 2 linear types of formulas using 10 and 11 measured distances. The standard deviations of the differences (calculated weight minus actual weight) range from 216 g to 219 g. The frequency of differences greater than +/- 15% of the calculated weight ranges between 3.0% and 4.3% of the cases. Miscalculations of more than 700 g (absolutely) have not been noted. In addition, five other formulas (logarithmic and linear types with 5 to 8 measurements) have yielded good results. Using 5 to 8 measurements, the logarithmic types of formulas are better than the linear ones. The mathematical types of formulas cannot achieve the improvements resulting from a greater number of measurements.

Birth Weight↗
PubMed2005

A mathematical model for tear drainage through the canaliculi.

PURPOSE: Tear drainage through the canaliculi has been extensively studied experimentally but there has been no attempt to develop a quantitative model for this process. In this paper, we develop a mathematical model for the tear drainage through the canaliculi. METHODS: The mathematical model is based on the experimental findings of Doane, according to which the muscle action during a blink drives the tear drainage. In this paper, mathematical models are developed for the tear flow and the canalicular deformation, and the model equations are solved to predict the tear drainage rates. RESULTS: The drainage rates depend on various physiological parameters. The time to attain a steady state during the drainage process can vary from about 0.0010 s to 0.0546 s, and the tear drainage rate can vary from 0.10 microl/min to 4.00 microl/min for a normal tear film, for physiologically reasonable values of various system parameters. CONCLUSIONS: The model predictions agree with various physiological experiments, at least qualitatively. The model also helps resolve the differences between various tear drainage experiments.

Blinking↗
PubMed2000

Experimental evaluation of a mathematical model for predicting transfer efficiency of a high volume-low pressure air spray gun.

The transfer efficiency of a spray-painting gun is defined as the amount of coating applied to the workpiece divided by the amount sprayed. Characterizing this transfer process allows for accurate estimation of the overspray generation rate, which is important for determining a spray painter's exposure to airborne contaminants. This study presents an experimental evaluation of a mathematical model for predicting the transfer efficiency of a high volume-low pressure spray gun. The effects of gun-to-surface distance and nozzle pressure on the agreement between the transfer efficiency measurement and prediction were examined. Wind tunnel studies and non-volatile vacuum pump oil in place of commercial paint were used to determine transfer efficiency at nine gun-to-surface distances and four nozzle pressure levels. The mathematical model successfully predicts transfer efficiency within the uncertainty limits. The least squares regression between measured and predicted transfer efficiency has a slope of 0.83 and an intercept of 0.12 (R2 = 0.98). Two correction factors were determined to improve the mathematical model. At higher nozzle pressure settings, 6.5 psig and 5.5 psig, the correction factor is a function of both gun-to-surface distance and nozzle pressure level. At lower nozzle pressures, 4 psig and 2.75 psig, gun-to-surface distance slightly influences the correction factor, while nozzle pressure has no discernible effect.

Air Pollutants, Occupational↗
PubMed2004

MAX meets ADAM: a dosimetric comparison between a voxel-based and a mathematical model for external exposure to photons.

The International Commission on Radiological Protection intends to revise the organ and tissue equivalent dose conversion coefficients published in various reports. For this purpose the mathematical human medical internal radiation dose (MIRD) phantoms, actually in use, have to be replaced by recently developed voxel-based phantoms. This study investigates the dosimetric consequences, especially with respect to the effective male dose, if not only a MIRD phantom is replaced by a voxel phantom, but also if the tissue compositions and the radiation transport codes are changed. This task will be resolved by systematically replacing in the mathematical ADAM/GSF exposure model, first the radiation transport code, then the tissue composition and finally the phantom anatomy, in order to arrive at the voxel-based MAX/EGS4 exposure model. The results show that the combined effect of these replacements can decrease the effective male dose by up to 25% for external exposures to photons for incident energies above 30 keV for different field geometries, mainly because of increased shielding by a heterogeneous skeleton and by the overlying adipose and muscle tissue, and also because of the positions internal organs have in a realistically designed human body compared to their positions in the mathematically constructed phantom.

Adult↗