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At least 253 records · Page 14Linked to original sources
PubMed1978

Dry-heat destruction of lipopolysaccharide: mathematical approach to process evaluation.

A mathematical model was developed to estimate the number of logarithmic cycles (LDec) of lipopolysaccharide concentration destroyed by a dry-heat sterilization process. The LDec values calculated from the mathematical model agreed well with those obtained from the destruction of lipopolysaccharide by a dry-heat treatment. A discussion of how the mathematical model may be used to evaluate a dry-heat sterilization cycle is presented. This mathematical model and the dry-heat destruction curves indicated existence of a maximum LDec value at each temperature. The implications of this finding are discussed.

Escherichia coli↗
PubMed1974

Mathematical estimation on the level of microbial contamination on spacecraft surfaces by volumetric air sampling.

Microbiological sampling methods presently used for enumeration of microorganisms on spacecraft surfaces require contact with easily damaged components. Estimation of viable particles on surfaces using air sampling methods in conjunction with a mathematical model would be desirable. Parameters necessary for the mathematical model are the effect of angled surfaces on viable particle collection and the number of viable cells per viable particle. Deposition of viable particles on angled surfaces closely followed a cosine function, and the number of viable cells per viable particle was consistent with a Poisson distribution. Other parameters considered by the mathematical model included deposition rate and fractional removal per unit time. A close nonlinear correlation between volumetric air sampling and airborne fallout on surfaces was established with all fallout data points falling within the 95% confidence limits as determined by the mathematical model.

Actinomycetales↗
PubMed2002

A mathematical model to detect inspiratory flow limitation during sleep.

The physiological significance of inspiratory flow limitation (IFL) has recently been recognized, but methods of detecting IFL can be subjective. We sought to develop a mathematical model of the upper airway pressure-flow relationship that would objectively detect flow limitation. We present a theoretical discussion that predicts that a polynomial function [F(P) = AP(3) + BP(2) + CP + D, where F(P) is flow and P is supraglottic pressure] best characterizes the pressure-flow relationship and allows for the objective detection of IFL. In protocol 1, step 1, we performed curve-fitting of the pressure-flow relationship of 20 breaths to 5 mathematical functions and found that highest correlation coefficients (R(2)) for quadratic (0.88 +/- 0.10) and polynomial (0.91 +/- 0.05; P < 0.05 for both compared with the other functions) functions. In step 2, we performed error-fit calculations on 50 breaths by comparing the quadratic and polynomial functions and found that the error fit was lowest for the polynomial function (3.3 +/- 0.06 vs. 21.1 +/- 19.0%; P < 0.001). In protocol 2, we performed sensitivity/specificity analysis on two sets of breaths (50 and 544 breaths) by comparing the mathematical determination of IFL to manual determination. Mathematical determination of IFL had high sensitivity and specificity and a positive predictive value (>99% for each). We conclude that a polynomial function can be used to predict the relationship between pressure and flow in the upper airway and objectively determine the presence of IFL.

Humans↗
PubMedDate not supplied

Mathematical derivative applied to international normalised ratio and analytical variations in oral anticoagulant therapy control.

A reliable prothrombin time (PT) testing and a careful drug dosage can prevent thrombotic or bleeding complications of the oral anticoagulant therapy. The international normalised ratio (INR) as PT standardisation introduced an analytical variation that increases with higher PT measures and higher international sensitivity index (ISI) values. Our study was conducted to investigate the INR accuracy through the mathematical derivative application to reduce the analytical component of the INR uncertainty. The evaluation of accuracy among four different systems (prothrombin activity percent, PT seconds, PT ratio and INR) was determined by the simulation of a systematic error. Plasma samples were diluted 1:2; then they were compared observed with the expected values. We analysed the calculation system of the INR through the mathematical derivative in 87 PT ratio measurements. The analytical incidence of thromboplastin ISI was performed through an elaboration of INR mathematical derivative considering 10 different ISI values ranging from 1.1 to 2. The data expressed as PT ratios revealed a lower systematic error propagation suggesting that a linear system is more accurate. According to the calculation formula of INR, analytical variability increases with the PT measurements, then with the intensity of anticoagulation. Mathematical derivative suggests that the INR uncertainty due to the ISI can be reduced using a thromboplastin reagent with a low ISI or with ISI close to 1.

Administration, Oral↗
PubMed1995

A mathematical analysis of haemorheologic factors during cardiopulmonary bypass for congenital heart disease.

Rheologic properties of blood are impaired by cardiac surgery using cardiopulmonary bypass. This study was set out to establish a mathematical model in order to assess seven known haemorheologic factors and evaluate their degrees of influence on blood rheology in cardiopulmonary bypass. Sixteen patients undergoing elective congenital cardiac surgery were studied. High shear blood viscosity, low shear blood viscosity, haematocrit, red blood cell filtration rate, red blood cell electrophoresis time, plasma viscosity and fibrinogen were monitored. The method for mathematical calculation was the stepwise regression analysis. The results showed that both high shear and low shear blood viscosity were mainly influenced by haematocrit and plasma viscosity. Red blood cell filterability contributed more than red blood cell electrophoresis time for low shear blood viscosity. The mathematical model was re-tested statistically and demonstrated that the selected factors in the model represented approximately 75% of rheologic changes during the surgery. Therefore, this mathematical analysis can be used to estimate the role of various possible haemorheologic factors and evaluate cardiopulmonary bypass techniques and therapeutic interventions.

Adolescent↗
PubMed2006

Mathematical modelling and numerical simulation of the morphological development of neurons.

BACKGROUND: The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other. METHODS: A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described. RESULTS: Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development. CONCLUSION: A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.

Animals↗
PubMed2005

Mathematical models use varying parameter strategies to represent paralyzed muscle force properties: a sensitivity analysis.

BACKGROUND: Mathematical muscle models may be useful for the determination of appropriate musculoskeletal stresses that will safely maintain the integrity of muscle and bone following spinal cord injury. Several models have been proposed to represent paralyzed muscle, but there have not been any systematic comparisons of modelling approaches to better understand the relationships between model parameters and muscle contractile properties. This sensitivity analysis of simulated muscle forces using three currently available mathematical models provides insight into the differences in modelling strategies as well as any direct parameter associations with simulated muscle force properties. METHODS: Three mathematical muscle models were compared: a traditional linear model with 3 parameters and two contemporary nonlinear models each with 6 parameters. Simulated muscle forces were calculated for two stimulation patterns (constant frequency and initial doublet trains) at three frequencies (5, 10, and 20 Hz). A sensitivity analysis of each model was performed by altering a single parameter through a range of 8 values, while the remaining parameters were kept at baseline values. Specific simulated force characteristics were determined for each stimulation pattern and each parameter increment. Significant parameter influences for each simulated force property were determined using ANOVA and Tukey's follow-up tests (alpha <or= 0.05), and compared to previously reported parameter definitions. RESULTS: Each of the 3 linear model's parameters most clearly influence either simulated force magnitude or speed properties, consistent with previous parameter definitions. The nonlinear models' parameters displayed greater redundancy between force magnitude and speed properties. Further, previous parameter definitions for one of the nonlinear models were consistently supported, while the other was only partially supported by this analysis. CONCLUSION: These three mathematical models use substantially different strategies to represent simulated muscle force. The two contemporary nonlinear models' parameters have the least distinct associations with simulated muscle force properties, and the greatest parameter role redundancy compared to the traditional linear model.

Journal Article↗
PubMed2005

The etiology of mathematical and reading (dis)ability covariation in a sample of Dutch twins.

The genetic etiology of mathematical and reading (dis)ability has been studied in a number of distinct samples, but the true nature of the relationship between the two remains unclear. Data from the Netherlands Twin Register was used to determine the etiology of the relationship between mathematical and reading (dis)ability in adolescent twins. Ratings of mathematical and reading problems were obtained from parents of over 1500 twin pairs. Results of bivariate structural equation modeling showed a genetic correlation around .60, which explained over 90% of the phenotypic correlation between mathematical and reading ability. The genetic model was the same for males and females.

Adolescent↗
PubMed1991

Mathematical modelling of competitive labelled-ligand assay systems. Theoretical re-evaluation of optimum assay conditions and precision data for some experimentally established radioimmunoassay systems.

A mathematical theory of competitive labelled-ligand assays was developed with the intention of theoretically re-evaluating the optimal assay conditions and precision data of assay systems established by experiment. Our theory is based upon the assumptions of a simple bimolecular reaction mechanism, homogeneous reactants, as well as kinetically indistinguishable labelled and non-labelled ligands. The general case of two-step (non-equilibrium) assay was considered including the one-step (equilibrium) assay as a special case. The solution of the system of corresponding kinetic differential equations was used to mathematically construct standard curves. Furthermore, intraassay precision profiles and indices as well as detection limits were calculated considering solely the pipetting error, epsilon, as a source of experimental error. A procedure was outlined to mathematically determine the optimal incubation conditions for any assay system targeted to a given analyte concentration, P, at which the standard deviation of assay results is to be minimized. Estimates of both the content of binding sites and the equilibrium constant, K, of the specific binding agent are necessary, and these can be derived from Scatchard plots. For six RIA systems, of which three were one-step and three were two-step assays, experimental assay conditions and precision data were compared with theoretical predictions. Experimentally determined antibody binding site concentrations agreed fairly well with those independently evaluated by mathematical optimization. Mean precision indices, defined as constituting an average over the complete precision profile, were found to be within the theoretically predicted range, i.e. two- to threefold the pipetting error.(ABSTRACT TRUNCATED AT 250 WORDS)

Binding Sites, Antibody↗
PubMed2006

A comparison of visual and mathematical detection of the electromyographic threshold during incremental pedaling exercise: a pilot study.

During exhaustive incremental pedaling exercises, root mean square or amplitude of integrated electromyographic values exhibits a nonlinear increase, i.e., the so-called electromyographic threshold (EMG(Th)). As proposed by various authors, this EMG(Th) could be used as a complementary indicator of the aerobic-anaerobic transition in physiological evaluations. However, most of these studies used visual detection for the EMG(Th) and to date no previous study has shown the reliability of this type of EMG(Th) detection. We aimed to compare a visual and a mathematical method for EMG(Th) detection in each of 8 lower limb muscles during incremental cycling exercise. Our results showed an overestimation in the number of cases in which EMG(Th) was detected when using visual inspection (n = 45) compared with the mathematical method (n = 32). However, no significant differences were observed between the 2 methods concerning the power output at which EMG(Th) occurred. These results suggest that EMG(Th) should be mathematically detected. In this context, coaches can easily perform such measurements in order to evaluate the impact of their training programs on the neuromuscular adaptations of their athletes. For example, an automatic mathematical detection of EMG(Th) could be performed during a pedaling exercise in order to detect neuromuscular fatigue. Furthermore, this index could be used during test or training sessions performed either in a lab or in ecological situations. Moreover, the use of EMG(Th) to predict ventilatory threshold occurrence could be an interesting tool for trainers who cannot use the very expensive devices needed to analyze respiratory gas exchanges.

Adult↗
PubMed2004

Mathematical model of cylindrical form tolerance.

Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y14.5.1M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of tolerance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.

Algorithms↗
PubMed2000

Mathematical models for assessment of long-term persistence of antibodies after vaccination with two inactivated hepatitis A vaccines.

Very few studies with inactivated hepatitis A vaccines were designed for long-term follow-up of antibody persistence. Based on the serological data from these vaccine trials, mathematical models were developed to predict the decrease of anti-hepatitis A virus (anti-HAV) antibodies after vaccination. This study was designed to compare Avaxim (0-6 months) to Havrix 720 (0-1-6 months). In this paper, both groups of vaccinees are described considering the age, gender, and weight of the subjects at enrollment. For mathematical modelling, two different approaches were used: one starting the calculations from the geometric mean titres (GMTs) at each point in time, the other basing the calculations on individual anti-HAV titres. Both vaccines are very immunogenic, although Avaxim shows a higher GMT at each point in time. When these data are used in mathematical models to predict the persistence of anti-HAV antibodies, both vaccines (Avaxim and Havrix 720) show similar long-term antibody kinetics. Antibody levels > or = 20 mIU/ml are estimated to last on average for at least 10 years after completion of the full vaccination course. Ten years after the full course, approximately 53% of subjects are estimated to have antibody levels > or = 20 mIU/ml. At 15 years, these levels will be maintained by about 34% of vaccinees. Avaxim and Havrix 720 show a similar long-term profile of persistence of anti-HAV. A mathematical model based on GMTs appeared to give equivalent results to a model based on individual serological data. The GMT method is easier to apply than the individual based method. However, the advantage of the latter method is the possibility of calculating confidence limits for the predicted values and making estimates of the percentage of subjects having a certain level of antibody titres at a certain time.

Adolescent↗
PubMedDate not supplied

Empirical and mechanistic mathematical models of temporal evolution of milk production in ruminants.

In the various sectors of animal science there has been little exploration of the theoretical mathematical aspects of data analysis and modelling. The dominant statistical methods used for the analysis of experimental data are rarely valuable for developing a deeper understanding of the problem. In addition they do not take account of the evolution over time of those variables of major interest to be studied. Only recently have more sophisticated methods of mathematical modelling begun to be used. Nonetheless attention tends to be focused exclusively on empirical models. Mathematical models with greater explanatory power, in particular those which use differential equations, are as yet little used. This work develops a mathematical approach to a problem that is of great interest in animal science: the development over time of milk production in economically important ruminant species.

Animals↗
PubMed2003

[Mathematics, milieu, text].

Greek theoretical mathematics emerges among sixth-century Ionians from a background of professional practitioners, concerned chiefly with arithmetical operations. Its characteristical features (impersonalization, standardization, diagrams) develop as part of an elitist play of distinction at fifth- and fourth-century Athens, mainly to ascertain the tradition of that knowledge without adequate institutions. Sophists challenge the mathematicians' practices, philosophers adopt the mathematicians' knowledge as a model of truth, but the mathematicians themselves remain autonomous. Even hellenistic mathematics, semi-institutionalized at royal courts, is little more than a private affair of a narrow circle of intellectuals. All this time the practitioners' traditions persist basically unaltered and constantly present the theoreticians with a social and epistemic background to differentiate "their" mathematics from. Finally, these two branches of Greek mathematics, a practical and a theoretical one, are describable as reciprocally systematized forms of knowledge.

English Abstract↗
PubMed2004

Mathematical correction of the invitro storage--related increase in erythrocyte mean cell volume of an automated hematology analyzer--the Cell-Dyn 4000.

The erythrocyte mean cell volume (MCV) increases during in vitro storage. In aged specimens that are processed in the hematology laboratory, this phenomenon can result in misclassification of erythrocyte size. The mean cell volume is closely correlated with the mean cell hemoglobin (MCH), which does not suffer the same degree of storage-related change. These two observations offer the opportunity to perform a mathematical prediction of the MCV in aged specimens. The mathematical correction proposed in this study uses the relationship MCV = MCHC (MCH concentration)/MCH. However, instead of using a constant value for MCHC, our approach has been further refined to take account of the weak but direct relationship between MCH and MCHC. The slope and y intercept of this relationship was derived by linear regression and then used to predict an idealized MCHC, which in combination with the MCH was used to derive a predicted MCV. This method was tested in samples from 209 hospital patients using the Cell-Dyn 4000 automated hematology analyzer. The observed MCV after 24 and 48 hours of room temperature storage were on average 6.7 and 11.6 fL higher than the MCV values of the samples when processed fresh. In contrast, the mean bias of the predicted MCV values after 24 and 48 hours was -0.1 and 0.9 fL, respectively. Our study also examined the use of the Cell-Dyn 4000 white cell viability fraction (WVF) as a means of predicting when to apply the mathematical correction. The WVF of the Cell-Dyn 4000 is based on fluorescent dye exclusion by viable leukocytes, which declines during storage. A WVF threshold of 0.95 successfully separatedthe fresh samples from those stored for 24 and 48 hours. For those laboratories who process aged specimens, this offers the opportunity to report the MCV in fresh samples, while predicting and mathematically correcting the MCV in samples that are affected by age-related storage changes.

Blood Preservation↗
PubMed2002

[The kinetic and mathematical model of PCR amplification experiment].

The PCR technique has been set up for nearly twenty years and is becoming more and more ripe. But because of the multiple influencing factors and complicated reaction procedures,no mathematical method that can describe the PCR reaction has been given. On the basis of its elementary principle,we suggested a kinetic equation to describe the reaction procedure,Wamp=[Ntarg x (1+P)n1+0.5 x Cenz x U x P x Ceactive x (n-nl)-Ntarg x (1+n x P)] x Cu x M. This equation can describe correctly the accumulation rule of PCR product and thus build up the kinetic-mathematical model of PCR reaction. The predicted CT value of PE 7700 by the kinetic-mathematical model was in accordance with the real value detected by the machine. This kinetic-mathematical model accompanied by proper detecting equipment and computer could make an automatic PCR instrument, which would produce much better result. A laboratory can predict the amount of PCR product by this model and provide accurate information for further handling of PCR product according to its own condition. In this model,the molecular basis that PCR reaction is doomed to change from exponential amplification to linear amplification had been clarified.

English Abstract↗
PubMed2005

Mathematical modelling of small wastewater treatment plants: power and limitations.

Although mathematical modelling of biological wastewater treatment processes has proved to be valuable for large-scale WWTPs (wastewater treatment plants) little experience has been acquired in the mathematical modelling of small wastewater treatment plants. This paper seeks to evaluate the applicability of mathematical modelling on small systems, which are characterized by high fluctuations in organic and hydraulic loads and little possibility for control. In order to achieve this, the paper examines the different steps in a general modelling protocol. One important bottleneck for the general use of mathematical modelling of small systems that emerges is the frequent sampling and many analyses needed for characterization of the flows while its applicability is limited. On the other hand, the determination of the model structure of a small WWTP can be quite valuable. Experiments show that tracer tests should include tests with a highly varying influent flow rate to spot independent small internal flows as these can have a significant impact on the behaviour of peak concentrations throughout the system. In addition, the model structure determination can provide useful information on dead zones, short-circuiting and mixing behaviour in the plant.

Models, Theoretical↗
PubMed2004

An improved mathematical approach for determination of molecular kinetics in living cells with FRAP.

The estimation of binding constants and diffusion coefficients of molecules that associate with insoluble molecular scaffolds inside living cells and nuclei has been facilitated by the use of Fluorescence Recovery after Photobleaching (FRAP) in conjunction with mathematical modeling. A critical feature unique to FRAP experiments that has been overlooked by past mathematical treatments is the existence of an 'equilibrium constraint': local dynamic equilibrium is not disturbed because photobleaching does not functionally destroy molecules, and hence binding-unbinding proceeds at equilibrium rates. Here we describe an improved mathematical formulation under the equilibrium constraint which provides a more accurate estimate of molecular reaction kinetics within FRAP studies carried out in living cells. Due to incorporation of the equilibrium constraint, the original nonlinear kinetic terms become linear allowing for analytical solution of the transport equations and greatly simplifying the estimation process. Based on mathematical modeling and scaling analysis, two experimental measures are identified that can be used to delineate the rate-limiting step. A comprehensive analysis of the interplay between binding-unbinding and diffusion, and its effect on the recovery curve, are presented. This work may help to bring clarity to the study of molecular dynamics within the structural complexity of living cells.

Fluorescence↗