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PubMedDate not supplied

[Objective assessment of biological aging in the human: results].

From a population sample of 139 healthy persons, six specially selected aging parameters were tested for their significance to vitality, by means of four mathematical models referring to the concept of vitality. As reference values, tm, is the age expressed in years when maximal vitality occurs, and the aging constant is beta, also known as an aging factor. Our results for tm extended from 16.6 to 39.6 years, depending on the respective mathematical model applied. We find a similar characteristic for the beta-values. A comparison with results in other publications on the subject, obtained by processing a considerably larger number of variables than we did, underlined the utility of our parameters. This is also shown by the quality of results we obtained by regression analysis, by the adjustment to the functions of the vitality concept and by the simplicity of the required laboratory methods of analysis.

Adult↗
PubMed1990

Limitations of the open loop gain concept in studies of respiratory control.

A steady state mathematical model was used to study the limitations of applying the open loop gain concept to the ventilatory control system. Open loop gain is a term used in the study of linear control systems and is an indicator of how well the controlled variable is regulated. The model contained descriptions of the O2 and CO2 control systems as well as their interactions. Disturbances to the system were modelled as occurring via inspired air, metabolic rate and ventilation. The ventilatory response to hypoxia was simulated for (a) hypocapnic hypoxia, (b) normocapnic hypoxia (PaCO2 = 40 torr) and (c) hypercapnic hypoxia (PaCO2 = 45 torr). The open loop gains of the O2 and CO2 loops were calculated at each operating point. In addition, the sensitivity of the controlled variable to disturbances to the loop were also compared. It was observed that open loop gain did not completely describe the characteristics of the ventilatory control system. This was due to the fact that the ventilatory system is nonlinear and the regulatory ability of the ventilatory system depends on the route of the disturbance, and (2) open loop gain ignores the interactions of the CO2 and O2 loops, which can be substantial.

Animals↗
PubMed2006

Quantitative real-time RT-PCR data analysis: current concepts and the novel "gene expression's CT difference" formula.

For quantification of gene-specific mRNA, quantitative real-time RT-PCR has become one of the most frequently used methods over the last few years. This article focuses on the issue of real-time PCR data analysis and its mathematical background, offering a general concept for efficient, fast and precise data analysis superior to the commonly used comparative CT (DeltaDeltaCT) and the standard curve method, as it considers individual amplification efficiencies for every PCR. This concept is based on a novel formula for the calculation of relative gene expression ratios, termed GED (Gene Expression's CT Difference) formula. Prerequisites for this formula, such as real-time PCR kinetics, the concept of PCR efficiency and its determination, are discussed. Additionally, this article offers some technical considerations and information on statistical analysis of real-time PCR data.

Benzothiazoles↗
PubMed2004

Practical introduction to record linkage for injury research.

The frequency of early fatality and the transient nature of emergency medical care mean that a single database will rarely suffice for population based injury research. Linking records from multiple data sources is therefore a promising method for injury surveillance or trauma system evaluation. The purpose of this article is to review the historical development of record linkage, provide a basic mathematical foundation, discuss some practical issues, and consider some ethical concerns. Clerical or computer assisted deterministic record linkage methods may suffice for some applications, but probabilistic methods are particularly useful for larger studies. The probabilistic method attempts to simulate human reasoning by comparing each of several elements from the two records. The basic mathematical specifications are derived algebraically from fundamental concepts of probability, although the theory can be extended to include more advanced mathematics. Probabilistic, deterministic, and clerical techniques may be combined in different ways depending upon the goal of the record linkage project. If a population parameter is being estimated for a purely statistical study, a completely probabilistic approach may be most efficient; for other applications, where the purpose is to make inferences about specific individuals based upon their data contained in two or more files, the need for a high positive predictive value would favor a deterministic method or a probabilistic method with careful clerical review. Whatever techniques are used, researchers must realize that the combination of data sources entails additional ethical obligations beyond the use of each source alone.

Databases, Factual↗
PubMed1994

The effect of mathematics and coordinate system on comparability and "dependencies" of nucleic acid structure parameters.

This paper critically examines the methodologies used to analyze nucleic acid three-dimensional structure based on guidelines set at a 1988 EMBO workshop. The implications of these analyses cannot be fully understood without a thorough knowledge of how the numbers are calculated. This paper addresses one aspect of the calculations, namely the observed correlations between various parameters. These correlations are addressed in the mathematics by explicitly incorporating the concept of a pivot point, which is the point about which a base rotates as it buckles, propeller twists and opens. Pivot points enable one to model the physical motion of bases more accurately. As a result, they greatly reduce and/or eliminate the statistical correlations between rotational and translational parameters found in other approaches. The correlations that are reduced or eliminated are actually artifacts of the mathematics employed and do not reflect true structural properties of nucleic acids. The mathematics we have developed, including the mathematics of pivot points, are presented in the companion paper. Here, we explain how some of the observed correlations occur as a by-product of the method of calculation, while others are truly structural, and we show how optimum pivot points can be determined to minimize artifactual correlations. The observation that experimental bases often rotate about the long axis in a "propeller" motion as well as rotate about the Z-axis of each base, "opening" into the major groove, is evident in the location of the optimum region for the pivot point as determined in this study. We consider locating a pivot point as a calibration step to increase the agreement between physical intuition and the mathematics of our program.

Base Sequence↗
PubMed2002

The competition-among-relations-in-nominals theory of conceptual combination: implications for stimulus class formation and class expansion.

One way in which new concepts are added to the conceptual system is through conceptual combination. The competition-among-relations-in-nominals (CARIN) theory (Gagné & Shoben, 1997) proposes that conceptual combination involves specifying a thematic relation (e.g., noun MADE OF modifier) to link the constituent concepts (e.g., chocolate and bee). This theory claims that relations have different strengths for various concepts that correspond to how often a modifier and relation have been paired in previous encounters with combined concepts and that this relational knowledge strongly affects the ease with which combined concepts can be formed. A mathematical model that incorporates key claims of the theory is presented, and empirical findings that are relevant to evaluating the CARIN theory are reviewed. The parallels between the CARIN theory and approaches to stimulus class formation are also discussed.

Association Learning↗
PubMed1992

A model of the control of cellular regeneration in the intestinal crypt after perturbation based solely on local stem cell regulation.

The control mechanisms involved in regeneration of murine intestinal crypts after perturbations are presently not well understood. The existence of some feedback signals from the cells on the villus to the cells in the crypt has been suggested. However, some recent experimental data point to the fact that regeneration in the crypt starts very early after perturbation, at a time when the villus cell population has hardly changed. In particular, this early cell proliferative activity is seen specifically at the bottom of the crypt, i.e. in the presumed stem cell zone and furthest from the villus. The objective of this study was to investigate whether a new concept of regulation operating solely at the stem cell level could explain the present mass of accumulated data on the post-irradiation recovery, which is an extensively studied perturbation from the experimental point of view. In order to check its validity, the new concept was formalized as a mathematical simulation model thus enabling comparison with experimental data. The model describes the cellular development from stem cells to the mature villus cells. As a basic feature it is assumed that the self-maintenance and the cell cycle activity of the stem cells are controlled by the number of these cells in an autoregulatory fashion. The essential features of the experimental data (i.e. the recovery with time and the consistency between different types of measurements) can be very well reproduced by simulations using a range of model parameters. Thus, we conclude that stem cell autoregulation is a valid concept which could replace the villus crypt feedback concept in explaining the early changes after irradiation when the damage primarily affects the crypt. The question of the detailed nature of the control process requires further investigation.

Animals↗
PubMedDate not supplied

[Pro and contra regarding the threshold/non-threshold mutagenic (carcinogenic) action of low-level ionizing radiation].

According to the analysis of epidemiological and experimental data there are evidences in threshold on criterion of mutagenic (in broad sense) ionising radiation action. A threshold takes place in the region of about 20-200 mGy concerning a dose in case of an acute exposure and in the region of the third order above a background level regarding a dose rate in case of chronic or prolonged exposure. Evidences in favour of linear non-threshold conception are based on primitive mathematical extrapolations and approximations of the study results, mainly, in the region of intermediate doses/dose rates. Besides real data in region of low doses are ignored. The latter has a reason in paradigm of stochastic damage action of ionising radiation and in underestimation of cell and organism protection-reparation systems action. Regarding axiomatic bases of ionising radiation action it is possible to conclude more reliable substantiation of the dual (positive-negative) nature and the threshold conception concerning ionising radiation action in comparison with the non-threshold one.

Animals↗
PubMed2002

Modeling prediction of membrane bioreactor process with the concept of soluble microbial product.

The existence of soluble microbial products (SMP) produced by microbial cultures involved in biological wastewater treatment process has been widely investigated. This paper aims to establish an available mathematical model by incorporating the SMP concept into the Activated Sludge Model (ASM) No. 3. Prediction of sewage treatment performance in membrane bioreactor process under intermittent aerobic condition by model simulation was presented, and the results provided a more comprehensive image for this process. It was found that SMP could not be ignored and it contributed about 15% of total COD in the reactor under HRT = 12 hr and SRT = 10 days condition. The model also provided reasonable simulation results for nitrogen, biomass concentration, and other treatment behaviors. Furthermore, the treatment performance can be predicted under various operating conditions by this proposed model.

Bioreactors↗
PubMed2001

UV dose distribution characterization using fractal concepts for system performance evaluation.

This paper presents a mathematical model for estimating the UV dose distribution delivered by continuous-flow UV disinfection processes. The model adopts fractal concepts and a stochastic method to simulate microorganism (particle) trajectories through the irradiation zone of an open-channel UV system. The irregularity of particle trajectories attributable to random movements was characterized by fractal dimension. In turn, trajectory-specific doses were calculated by integrating UV intensity over travel time. Results of these simulations indicated that radiation intensities along the trajectories could be highly variable. Therefore, microorganisms are expected to receive a broad range of radiation doses as a result of variations in radiation intensity along their trajectories and spatial heterogeneity in the radiation intensity field. This supports previous assertions that the conventional averaged-dose approach will result in substantial deviations between predicted and actual system performance. Implications of the results in terms of treatment efficiency and system design are discussed. The presented approach is found to be useful as a tool for rapid estimation of the dose distribution delivered by UV processes.

Bacteria↗
PubMed2004

The maxslope taxometric procedure: mathematical derivation, parameter estimation, consistency tests.

This article first explains concepts in taxometrics, including the meaning of "taxon" in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regression slope (MAXSLOPE point) and the HITMAX cut, i.e., the point on a variable which, if used as a diagnostic cut-off score, yields maximum classification accuracy, is analyzed. A sufficient condition is given for the MAXSLOPE point to equal the HITMAX cut; however, most distributions have different MAXSLOPE and HITMAX points. Equations and an algorithm are spelled out for making a graphical test for the existence of a taxon, estimating taxometric parameters, and conducting consistency tests; the latter serve as stringent checks on the validity of a taxonic conjecture. The plausibility of assumptions made, in deriving MAXSLOPE equations, is discussed, and the qualitative effects of violations of these assumptions are explained.

Classification↗
PubMed1986

The "protocell": a mathematical model of self-maintenance.

The concepts of self-generation, autonomous boundary and self-maintenance are explained briefly. The "protocell" is presented as a model of self-maintenance which is based on simple physical mechanisms of diffusion and reaction. The time evolution of the surface of the protocell is taken into account explicitly in the form of a Stefan condition giving rise to a non-linear feedback of the surface motion to the reaction and diffusion processes inside the protocell. The spatio-temporal dynamics are investigated, particularly in the neighbourhood of the stationary states, showing a self-maintaining behaviour under a certain range of nutritional conditions. Under another set of conditions we find an instability leading to a division process so that the population of protocells becomes self-maintaining instead of the single individual. The presented formulation of the protocell model is crucially improved compared with a previous version which required boundary conditions at infinity. The previous version was not strictly self-maintaining since dynamics outside the cell were essential for its behaviour.

Animals↗
PubMed1996

Intraoperative bleeding: a mathematical model for minimizing hemoglobin loss.

BACKGROUND: The rationale for intraoperative blood transfusion is often based on incorrect concepts and criteria. STUDY DESIGN AND METHODS: A mathematical model based on physiologic measures and describing the usual pattern of surgical blood loss is presented, and a theoretical means of minimizing intraoperative hemoglobin loss with hypervolemic hemodilution is proposed. RESULTS: Intraoperative hemoglobin loss is often overestimated especially in connection with high-volume blood loss. The model of intraoperative hypervolemic hemodilution shows significant improvement in hemoglobin concentration in the immediate postoperative period, compared with normovolemic conditions. The difference is most marked at a high volume of blood loss and a high degree of maintained hypervolemia. CONCLUSION: The practice of intraoperative blood transfusion according to volume of blood lost is to be discouraged, and regular monitoring of the hematocrit is necessary to avoid unnecessary transfusion. The theoretical advantages of hypervolemic hemodilution warrant further testing of the model in a clinical setting.

Blood Loss, Surgical↗
PubMed1994

A general formulation of the concept of independent action for the combined effects of agents.

Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent action is close to the literal meaning of the term "non-interaction". Since this concept does not depend on the mechanisms of actions nor on the type of effect scale used, it is suitable as one of the basic criterion for the definition of synergism and antagonism. A general mathematical framework of independent action is presented in this paper based on the concept of "relative effect" as used in the literature. The different equations for independent action currently used in various areas are shown to be manifestations of a general formula under different sets of boundary conditions, which are the natural limiting values of the effects of the corresponding system observed at low and at high doses of the agents. The framework can be generalized to the combined action of n-agents as well as to the interaction of an agent with itself. In addition, the differential form of the formula for independent action is derived. This framework of systematic definitions and derived equations enable a more in-depth study of the implications of the concept of independent action and its relation to other concepts of non-interaction.

Animals↗
PubMed1988

Analysis of PCO2 variations in the renal cortex. II. Countercurrent exchange.

In an effort to explain the relatively high values of CO2 partial pressure (PCO2) that have been measured in the superficial renal cortex of the rat, we developed a mathematical model based on the concept of countercurrent exchange between blood vessels. The model includes the possibility of exchange of CO2 between interlobular arteries and veins throughout the cortex, and between "terminal" arterioles and venules (those associated with the most superficial nephrons). The effect of countercurrent exchange is to amplify the increases in PCO2 that occur in the microcirculation of individual nephrons, which are due to the addition of metabolic CO2 and reabsorbed HCO3- and CO2 to peritubular capillaries. The model is formulated in terms of correlations that describe blood buffering equilibria in peritubular capillaries and in interlobular arteries and veins, and steady-state mass balances for the interlobular vessels. By use of physically reasonable vascular permeability values, simulations for the normal euvolemic Munich-Wistar rat yielded values of the surface-to-arterial PCO2 difference (delta PCO2) comparable to previously measured values. Predicted variations in delta PCO2 with afferent arteriolar blood flow rate and systemic arterial PCO2 were also in accord with available data. These results suggest that the amplifying effect of countercurrent exchange is in fact adequate to explain the high values of PCO2 measured in surface structures. The solutions to the mass balance equations are in closed analytical form and can be readily adapted to describe countercurrent exchange in the renal cortex of solutes other than CO2.

Animals↗
PubMed2002

Sphericity governs both stereochemistry in a molecule and stereoisomerism among molecules.

The concept of sphericity and relevant fundamental concepts that we have proposed have produced a systematized format for comprehending stereochemical phenomena. Permutability of ligands in conventional approaches is discussed from a stereochemical point of view. After the introduction of orbits governed by coset representations, the concepts of subduction and sphericity are proposed to characterize desymmetrization processes, with a tetrahedral skeleton as an example. The stereochemistry and stereoisomerism of the resulting promolecules (molecules formulated abstractly) are discussed in terms of the concept of sphericity as a common mathematical and logical framework. Thus, these promolecules are characterized by point group and permutation group symmetry. Prochirality, stereogenicity, prostereogenicity, and relevant topics are described in terms of the concept of sphericity.

Journal Article↗