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At least 217 records · Page 12Linked to original sources
PubMed1996

Thoughts about judging dialysis treatment: mathematics and measurements, mirrors in the mind.

This article considers the contributions of the urea kinetic parameters, , Kt/V and nPCR, to beliefs about judging dialysis treatment. The values calculated from any set of data depend on the model (eg, 1 pool, 2 pool, or so forth) and the mathematics used to derive the values. Yet, the medical community debates the value of Kt/V at which patients should be treated even as they debate the mathematics by which Kt/V should be calculated. The resulting ambiguities about proper targets and methods may actually frustrate large-scale clinical quality enhancement initiatives. The casual use of mathematical models can mislead unwary clinicians and compromise quality enhancement. For example, the observation that a high Kt/V is associated with a high nPCR leads to the widespread belief that improving Kt/V must substantially improve nutritional status. The association, however, results mainly, if not solely, from mathematical coupling rather than biological cause and effect. The misguided belief could contribute to ineffective treatment of malnourished patients. Complicated mathematical models are useful tools for describing and evaluating evolving concepts about the physical properties of dialysis and for estimating the effects of new therapies. However, the changing nature of concepts, and therefore the mathematical models designed to support them, makes clinical care ideas that attempt to shoehorn old concepts into new equations. It is the result of the dialysis treatment, not the mathematical path by which it is achieved, that is associated with improved patient health. Consequently, clinical care should be guided by simple measurements that reflect the outcome of the treatment, not by mathematical parameters.

Humans↗
PubMed1987

Information compression in biological systems.

In biological systems a high coordination between their individual parts occurs. The concept of coordination can be given a rigorous mathematical basis by the concept of order parameters and the slaving principle. We calculate the information of the total system in terms of order parameters and slaved subsystems. When qualitative changes of a system happen, the information change is given by that of the order parameters alone and may amount to few bits only.

Animals↗
PubMed2002

Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.

A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young's experiment.

Journal Article↗
PubMedDate not supplied

A theoretical framework for defining some concepts in evolution.

We present a theoretical framework for biological evolution with the intention of giving precise mathematical definitions of some concepts in evolutionary biology such as fitness, evolutionary pressure, specialization and natural selection. In this framework, such concepts are identified with well-known mathematical terms within the theory of dynamical systems. We also discuss some more general implications in evolution; for instance, the fact that our model naturally exhibits a frequency spectrum of the type 1/f for low frequencies of evolutionary events.

Algorithms↗
PubMedDate not supplied

[Revised version of the of the concept of digesting mental information].

The concept of information metabolism was introduced by prof. Kepiński at the end of the 1960-ies of the 20th century. The article presents the synthesis of a series of papers aiming to concrete, update and describe in mathematical terms the concept of metabolism of information. Theoretical basis of the model in the context of the theory of information and the main structures and functions of the metabolism of information are presented. These structures are: control centre (nucleus), boundaries (cell membrane), functional structures (endoplasmic reticulum), energy centres (mitochondria), synthesis centres (ribosoms) and elimination centres (lysosoms). At the end, the publications on the mathematical description of the information metabolism model are presented and discussed.

Brain↗
PubMedDate not supplied

Mathematical programming assisted drug design for nonclassical antifolates.

A concept from optimization theory, specifically, mathematical programming, is proposed for designing drugs with desired properties. The mathematical programming formulation is solved to obtain the optimal descriptor values, which are employed in the Cerius(2) modeling environment to infer the optimal lead candidates, in the sense that they exhibit both high selectivity and activity while ensuring low toxicity. It has been observed that unique substituent groups and their molecular conformations are responsible for attaining the goal of simultaneous high selectivity and activity. Both linear and nonlinear quantitative structure activity relationships (QSARs) have been developed for use in the proposed approach. A comparative study of these models is done, and it is shown that the QSARs are well represented by nonlinear models. The proposed mathematical programming strategy has been demonstrated for a class of nonclassical antifolates for Pneumocistis carinii and Toxoplasma gondii dihydofolate reductase. Some of the potential leads found in this study have biological properties similar to those in the open literature. We believe the technique proposed is general and can be applied to other structure based drug design.

Algorithms↗
PubMed1987

The effects of assertive training on performance in highly anxious adolescents.

The effects of assertive training on measures of assertiveness, state anxiety, and mathematics performance in highly anxious adolescents were investigated. A group of 96 highly anxious 9th graders was assigned to one of four treatment groups. Pretest and posttest assessment included the Adolescent Self-Expression Scale (a measure of assertiveness), the State-Trait Anxiety Inventory, and the Mathematics Problems and Concepts subtests of the California Achievement Test. Experimental treatment consisted of four assertive training sessions, while placebo treatment for the control groups consisted of four career development training sessions. Posttest was administered to all four groups. A MANOVA was used to analyze all of the data on the students who took the pre- and posttest and attended two or more training sessions. Assertive training resulted in increased assertiveness and decreased state anxiety, with no significant effect on mathematics performance, and no significant effect due to sex. It was concluded that assertive training is a counseling technique which can be used effectively with 9th graders.

Achievement↗
PubMedDate not supplied

Accuracy of conceptual age estimation from fetal crown-rump length.

The accuracy of conceptual age estimated by crown-rump length is not fully assessed by Robinson and Fleming in their excellent study. They avoid the problem by using the expression "menstrual maturity." We have evaluated predictors of fetal age from crown-rump length measurements where conceptual age was calculated either from the day of artificial insemination by donor (AID) or from the day of ovulation as judged from recordings of basal body temperature (BBT). When the date of AID was used as the conception date, better mathematical fits (R2 = 0.92) were obtained than when the thermal nadir was used (R2 = 0.86). The distribution around the regression line in the AID group is skewed with the 5th-95th percentile range being 3.7 days above the line and 7.3 days below the line. Similar results were obtained in the BBT group. Possible reasons for these findings are discussed.

Body Temperature↗
PubMed2006

The design of intracellular oscillators that interact with metabolism.

Biological oscillations such as circadian rhythms are ubiquitous in nature and have attracted significant attention because of their intriguing dynamics and important biological roles. Understanding of such sophisticated and robust oscillators requires more than the traditional reductionist approach. Recently, a synthetic approach similar to the design of engineering machinery has provided a valuable alternative for testing hypothetical operating principles. These man-made genetic circuits and gene-metabolic circuits are designed based on physical concepts, guided by mathematical models, and constrained by biological and chemical reality. While still primitive compared with the natural circuits, the designed gene-metabolic oscillator has begun to show hallmarks of circadian rhythms such as temperature compensation and close interaction with metabolism.

Animals↗
PubMed1992

Multimodality imaging and intracranial EEG display for stereotactic surgery planning in epilepsy.

We describe a computer program for stereotactic surgery planning based on multimodality imaging and the display of intracranial EEG data in relation to anatomical data. The program is primarily designed to be used by surgeons to assist them in localizing brain structures and plan the safe and accurate insertion of surgical tools and depth electrodes. The mathematics underlying these concepts are briefly described. Estimates of the accuracy of the procedures are calculated and made available to the user. An extension of the program was developed to integrate intracranial EEG data with conventional images in order to help the neurologist and neurosurgeon in visualizing the EEG data in relation to the anatomy. It can be used to visualize the measured EEG voltages, or processed signals such as the application of the tetrahedral field calculation, which provides an extension of conventional bipolar EEG to 3 dimensions.

Brain↗
PubMed2005

Development and evaluation of an ODL course on Medical Image Processing.

Recent developments in the field of Biomedical Engineering have led to considerable improvement in health care delivery, but also impose continuous change and improvement in education and training schemes of its professionals, in order to assure appropriate front-line knowledge, competencies and skills. Open and distance learning provides a very effective means for continuous education and training purposes. Image processing may be used as an attractive case for exploring the Collaborative Learning Model (CLM) paradigm in Open Distance Learning (ODL). An on-line course on Medical Image Processing, following the principles of collaborative learning, has been developed and evaluated. Each concept of the course is available in three levels of complexity. The first level shows only a very general description, actually the main idea. If the user is interested to continue, a second level is accessible, where the concept is explained in a more detailed manner. Moreover, for some concepts requiring complicated mathematical proofs, a third level is available. The course has been used at the European Course on Biomedical Engineering organized by the Department of Medical Physics, University of Patras, Greece, and was positively evaluated by the students.

Biomedical Engineering↗
PubMed2005

Kinetics of ultrasonic extraction of extractive substances from garden (Salvia officinalis L.) and glutinous (Salvia glutinosa L.) sage.

The kinetics of ultrasonic extraction of extractive substances (ES) from dry herbs of garden (Salvia officinalis L.) and glutinous (Salvia glutinosa L.) sage using petroleum ether, 70% ethanol or water at 40 degrees C, as well as the composition of dry extracts, were studied. The mechanism of ultrasonic extraction is confirmed to occur in two steps: first, dissolution of the ES near the particle surface (washing) and, second, diffusion from the solid particles to the bulk of the liquid extract (slow extraction). The process is described mathematically using three concepts of the unsteady diffusion through plant material, the film theory and the empirical equation of Ponomaryov. The yield of ES increases with increasing solvent polarity, and nearly the maximum concentration of ES in liquid extracts is achieved for about 20 min. The composition of extracts depends on both the extraction conditions applied and the plant material.

Kinetics↗
PubMed2002

A mathematical explanation of an increase in bacterial swimming speed with viscosity in linear-polymer solutions.

Bacterial swimming speed is sometimes known to increase with viscosity. This phenomenon is peculiar to bacterial motion. Berg and Turner (Nature. 278:349-351, 1979) indicated that the phenomenon was caused by a loose, quasi-rigid network formed by polymer molecules that were added to increase viscosity. We mathematically developed their concept by introducing two apparent viscosities and obtained results similar to the experimental data reported before. Addition of polymer improved the propulsion efficiency, which surpasses the decline in flagellar rotation rate, and the swimming speed increased with viscosity.

Bacteria↗
PubMedDate not supplied

A comparison of partial order technique with three methods of multi-criteria analysis for ranking of chemical substances.

An alternative to the often cumbersome and time-consuming risk assessments of chemical substances could be more reliable and advanced priority setting methods. An elaboration of the simple scoring methods is provided by Hasse Diagram Technique (HDT) and/or Multi-Criteria Analysis (MCA). The present study provides an in depth evaluation of HDT relative to three MCA techniques. The new and main methodological step in the comparison is the use of probability concepts based on mathematical tools such as linear extensions of partially ordered sets and Monte Carlo simulations. A data set consisting of 12 High Production Volume Chemicals (HPVCs) is used for illustration. It is a paradigm in this investigation to claim that the need of external input (often subjective weightings of criteria) should be minimized and that the transparency should be maximized in any multicriteria prioritisation. The study illustrates that the Hasse diagram technique (HDT) needs least external input, is most transparent and is least subjective. However, HDT has some weaknesses if there are criteria which exclude each other. Then weighting is needed. Multi-Criteria Analysis (i.e. Utility Function approach, PROMETHEE and concordance analysis) can deal with such mutual exclusions because their formalisms to quantify preferences allow participation e.g. weighting of criteria. Consequently MCA include more subjectivity and loose transparency. The recommendation which arises from this study is that the first step in decision making is to run HDT and as the second step possibly is to run one of the MCA algorithms.

Chemical Industry↗