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At least 451 records · Page 25Linked to original sources
PubMed2003

AIDS vaccines that allow HIV-1 to infect and escape immunologic control: a mathematic analysis of mass vaccination.

Cytotoxic T lymphocyte (CTL)-based HIV vaccine concepts shown to reduce viremia and postpone disease but not to prevent infection in monkeys are currently in human phase 1 trials. To evaluate the potential efficacy of vaccines that cannot prevent HIV-1 to infect and escape immunologic control, we designed a mathematic model that correlates the level of viremia to both infectiousness and disease progression. We speculate that vaccinees will have a virologic set point and disease progression rates comparable to untreated HIV-1-infected individuals with the best prognosis. Our model (illustrated with R0 = 3) shows that a sexually active population can ultimately be reduced to 26% of its initial size as a result of AIDS-related mortality in the absence of treatment or vaccination. Start of vaccination when HIV-1 prevalence is still low might postpone the peak incidence of infection and the dramatic decline in population size by up to 22 years. In conclusion, CTL-based vaccines that do not prevent HIV-1 infection but do postpone the time to onset of AIDS have considerable potential to curb the spread of HIV-1 and to postpone high AIDS-related mortality on a population level. The number of long-term survivors is substantially increased only when vaccination is initiated early in an AIDS epidemic, however.

AIDS Vaccines↗
PubMed2004

Network-based regulatory pathways analysis.

MOTIVATION: A useful approach to unraveling and understanding complex biological networks is to decompose networks into basic functional and structural units. Recent application of convex analysis to metabolic networks leads to the development of network-based metabolic pathway analysis and the decomposition of metabolic networks into metabolic extreme pathways that are true functional units of metabolic systems. Metabolic extreme pathways are derived from limited knowledge of the metabolic networks, but provide an integrated predictive description of metabolic networks. It is important to extend the concept of network-based metabolic pathways to genetic networks and develop mathematical procedures for network-based regulatory pathway analysis. RESULTS: We have established Kirchhoff's first law in genetic networks and introduced a concept of gene flows using matrix decomposition method. The Kirchhoff's first law provides the theoretical foundations for mathematical framework for development defining network-based regulatory pathways, and applying convex analysis in decomposing the genetic networks into regulatory extreme pathways. We presented a new approach to characterize the extreme pathway and developed a new algorithm for identifying a set of extreme pathways. Convex analysis and extreme pathway structure provide a unified framework for functional and structural analysis of metabolic and genetic networks, which will increase our ability to analyze, interpret and predict the function of metabolic and genetic networks. The proposed models for network-based regulatory pathway analysis have been applied to apoptosis regulatory network.

Algorithms↗
PubMed2005

The potential for mathematical modelling in the assessment of the radiation dose equivalent of cytotoxic chemotherapy given concomitantly with radiotherapy.

The linear quadratic (LQ) concept of biological effective dose (BED) is used with Poisson statistics to estimate the radiation equivalent BED of cytotoxic chemotherapy (CBED) that would provide improvements in tumour control probability (TCP) typically achieved in randomized clinical trials of chemoradiation. The concepts of pure radio-sensitization and independent chemotherapy cell kill are represented by mathematical equations. Small values of sensitizer enhancement ratios (s) can provide modest increases in TCP when large numbers of radiotherapy fractions are sensitized; larger s values are required if only a small number of radiotherapy fractions are sensitized. Independent chemotherapy induced cell kill is sufficient to explain the benefits achieved with concomitant chemoradiotherapy in situations where a sufficiently high chemotherapy dose intensity is used (i.e. the dose-time intensity of cytotoxic chemotherapy without radiation is considered to be sufficient to cause significant tumour regression although not cure). Care is required in the use of the Poisson cure probability model because of the associated steep dose-response curves that may underestimate both s and the CBED. By use of random sampling methods and estimation over a theoretical population of different tumours, more robust results are obtained with dose-response curves that correspond better to those in clinical data sets. These predict a 2-4 Gy(10) equivalent for each pulse of chemotherapy such as single agent Cis-Platinum when used weekly during radiotherapy for a maximum of 4 cycles. This preliminary paper does not consider normal tissue complication probabilities, of which there are relatively few mature results for modern chemoradiotherapy. The BED concept can be used to estimate the equivalent dose of radiotherapy that will achieve the same cell kill as concomitant cytotoxic chemotherapy. Relatively simple radiobiological modelling can be used to guide decision-making regarding the assessment of the most appropriate combined modality schedules, and has important implications in the design of clinical trials.

Antineoplastic Agents↗
PubMed2007

Why does placing the question before an arithmetic word problem improve performance? A situation model account.

The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve arithmetic word problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. In addition, this effect was more marked in the case of children who had poorer mathematical skills and in the case of more difficult problems. We argue that this pattern of results is compatible only with the situation or mental model theory, and not with the schema theory.

Analysis of Variance↗
PubMed1983

Role of similarity principles in data extrapolation.

This paper addresses the problem of extrapolating from data set gathered on a particular system to problems of more general physiological interest. It asks: what are the limits of the extrapolability of data? Under what circumstances can data derived from a particular system be transformed into data about another, different system? Such questions address the general problem of similarity analysis. A mathematical exploration of the meaning and usefulness of the concept of similarity is presented, and the necessity for a "prototype" is introduced. The discussion shows what we mean by the relationship between natural systems and the purest form of model of such systems, the mathematical model. The value and limitations of Dimensional Analysis are considered. It is concluded that the principle of dimensional homogeneity which underlies Dimensional Analysis is not strong enough to cope effectively with situations involving many phases, as arise in biological studies. Therefore, a more general approach is used. It is shown that the problems associated with data extrapolation are very deep and lead to some of the deepest issues in all of science. The extrapolation of data from animal models to human beings has been a general characteristic of pharmacologic research and, for that matter, biomedical investigations generally. Attention to limitations and dangers of such extrapolations seems overdue. With proper understanding of the essential nature of the extrapolatory action, and modeling relations, models can be validated.

Animals↗
PubMed1979

Seasonal migration and seasonal variation in fecundability: effects on birth rates and birth intervals.

Seasonal patterns in conception rates have been documented in several recent studies. In this paper, a mathematical model of the reproductive process is developed through which the impact of such variation in conception rates is assessed. It is found that the effect on fertility can be quite substantial, but that the birth rate when seasonal variation is occurring is approximated well by the birth rate calculated when conception rates are constant at their mean. These results indicate that further documentation of seasonality in conception rates and exploration of the causes of these patterns and their change is an important area for demographic research.

Birth Rate↗
PubMed2006

Developmental and individual differences in pure numerical estimation.

The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1, kindergartners and 1st, 2nd, and 3rd graders were presented problems involving the numbers 0-100; in Experiment 2, 2nd and 4th graders were presented problems involving the numbers 0-1,000. Parallel developmental trends, involving increasing reliance on linear representations of numbers and decreasing reliance on logarithmic ones, emerged across different types of estimation. Consistent individual differences across tasks were also apparent, and all types of estimation skill were positively related to math achievement test scores. Implications for understanding of mathematics learning in general are discussed.

Achievement↗
PubMed1988

Antigenic relationships between avian paramyxoviruses. III. A mathematical model of antigenic drift and a computer-assisted approach for construction of a phylogenetic tree.

The suggested model of antigenic kinship between related paramyxoviruses is based on another concept of antigenic determinant, as compared to the previously suggested combinatorial mathematical model by the authors. According to it, antigenic changes of any determinant do not proceed by "leaps" but can be changed gradually. Such changed determinant can induce a correspondingly changed type of antibodies which still preserve a certain kinship to the original type of the determinant (before its changing) revealed by cross reaction serological tests. Accordingly, there can be "families" of the determinants differing by degree of relatedness to (or, reversely, by antigenic distance from) the "original" ("ancestor") determinant. In addition to another interpretation of the antigenic kinship, the new mathematical model was used as an approach for revealing phylogenetic relationships between antigenically related viruses.

Antigens, Viral↗
PubMed1983

A unifying concept for carcinogenic risk assessments.

Carcinogens influence both the initiation of abnormal cells and the subsequent promotion of such cells into neoplasia. Certain other insults seem limited to the stimulation of cellular proliferation and of carcinogenic potentiation. Common examples include surgical, mechanical, chemical, and temperature wounding of tissue followed by healing. In addition, certain hyperplastic growth induced by some chemicals may also enhance tumorigenesis. We propose that the quantification of carcinogenic potentiation may derive from a common-index-quantity estimated according to enhanced cell proliferation resulting from cytotoxicity or toxic hyperplasia induced by a specific exposure. At this time, it is not possible to define, in a restrictive sense, the molecular events which are critical to potentiation but the processes of cell proliferation resulting from cytotoxicity/hyperplasia seem to serve as indices which contain the necessary (and perhaps several secondary) biological responses. The unique advantage is that cell-culture, animal, and human-level studies can be used to evaluate certain parameters of the mathematical model for an untested treatment protocol or chemical insult suspected to be a cofactor in tumorigenesis. The main thrust of this paper is to propose that tumorigenesis should be studied in terms of cellular-population kinetics in response to a biological challenge rather than according to chemical or energetic parameters of that challenge. This approach leads to mathematical equations which can serve as a unifying concept for carcinogenic risk assessments. Sample results, to illustrate the utility of this model, are given for polynuclear aromatic hydrocarbons, trace metals, ionizing radiations, CO, NO, SO2, O3, and NO2. Treatment, here, is for acute exposure conditions, but because the model is mechanistic, other exposure protocols can be addressed by simply adjusting some of the mathematical parameters according to factors estimated from a relative potency comparison of in vitro and in vivo studies best suited to the particular application of interest.

Animals↗
PubMedDate not supplied

Key concepts in biostatistics: using statistics to answer the question "is there a difference?".

Biostatistics seeks to answer the question "Is there a difference?" in the rate of a disease or characteristic among subgroups of patients. The goal of this article is to introduce and define measures used in epidemiology and discuss different types of analyses in clinical research with an emphasis on the concepts and implications of the analyses rather than the mathematics. The implications of the use of measures such as incidence and prevalence, as well as odds, risk, and hazards ratios may affect study conclusions. An understanding of the distinction between these summary measures is essential. The concepts of univariate and multivariate analyses, a discussion of what it means to control for potential confounders, and a description of statistical power and significance are also presented. These concepts are integral to the design and analysis of clinical studies. An understanding of their advantages and applications will enhance the reader's ability to understand and evaluate the literature.

Analysis of Variance↗
PubMed1990

A componential analysis of an early learning deficit in mathematics.

This study was designed to assess strategy choice and information-processing differences in normal and mathematically disabled first and second grade children. Twenty-three normal and 29 learning disabled (LD) children solved 40 computer-presented simple addition problems. Strategies, and their associated solution times, used in problem solving were recorded on a trial-by-trial basis and each was classified in accordance with the distributions of associations model of strategy choices. Based on performance in a remedial education course, as indexed by achievement test scores, the LD sample was reclassified into a LD-improved group and an LD-no-change group. No substantive differences comparing the normal and LD-improved groups occurred in the distribution of strategy choices, strategy characteristics (e.g., error rates), or rate of information processing. The performance characteristics of the LD-no-change group, as compared to the two remaining groups, included frequent counting and memory retrieval errors, frequent use of an immature computational strategy, poor strategy choices, and a variable rate of information processing. These performance characteristics were discussed in terms of the strategy choice model and in terms of potential long-term memory and working memory capacity deficits. In addition, implications for remedial education in mathematics were discussed.

Achievement↗
PubMed1995

[Diagnosis of performance anxiety in educational spelling tests: new results of the psychometric properties and validity of a relevant brief scale].

In the present study the psychometric properties and the criterion-related validity of a short scale for measuring students' spelling-specific test anxiety were analyzed. This scale consists of 13 self-rating items which reflect students' worry and emotionality reactions in face of spelling requirements at school. Along with some concurrent criterion variables (such as general self-esteem, academic and spelling-related self-concept, and spelling-related attributions, spelling and mathematics achievement, regressive classroom behavior), data were gathered at the beginning (N = 274) and, nearly 11 months later, at the end (N = 257) of the school year. At both measurement times, principal component analyses correspondingly revealed one common test anxiety factor and led to an overall scale format. This final scale solutions appeared to be sufficiently reliable and stable. Furthermore, their relationships to the various criterion variables largely turned out as theoretically expected. Especially, the spelling-specific test anxiety scores could be best predicted by spelling-specific self-concept and by spelling achievement, respectively. Thus, the findings of the present study could replicate the results of a previous pilot study and provided further support for the construct validity of interpretations based upon the spelling-specific test anxiety scale.

Anxiety↗
PubMed1982

A new approach to sterilization conditions. The IMO concept.

The sterilization requirements for medical/pharmaceutical applications are traditionally based on an extensive overkill. In the past few years, however, an evolution towards bioburden related sterilization processes has been started (F0 theory). Especially manufacturers of large volume parenterals have - forced by the thermolability of the product - contributed to this development. In this paper both philosophies are combined, resulting in a concept in which the bacteriological and physical bases of the sterilization process are mathematically related by using the F0 theory and by introducing an Imaginary Micro-Organism (IMO). The IMO concept provides the opportunity for anyone in the field of sterilization to raise the quality control level, which can be achieved by: - selecting optimum sterilization conditions without performing pre-sterilization counts: - step by step introducing the pre-sterilization count which results in even more favourable sterilization conditions.

Geobacillus stearothermophilus↗
PubMed1984

Fluid mechanics of the pulmonary circulation.

Assessment of the fluid mechanics of the pulmonary circulation has been hindered by the relative inaccessibility of the pulmonary vascular bed. Current understanding is based largely on analyses of mathematical models which have been used to simulate hemodynamic characteristics within an architectural representation of that bed. These representations have ranged from simple, lumped parameter structures to anatomically realistic structures based on measurements of casts of the irregular branching network of pulmonary arteries and veins. Nonlinear models have been studied to determine the effects of vessel taper and within beat geometrical variations as cross-sectional shapes change from circular to elliptical and small vessels undergo recruitment, distention, and collapse as a result of the shifting balance in alveolar, pleural, and capillary pressures. This article reviews current concepts of pulmonary circulatory fluid mechanics focusing on mathematical models and relevant hemodynamic studies.

Adolescent↗
PubMed1999

Beyond psychophysics: the need for a cognitive engineering approach to setting limits in manual lifting tasks.

The classical psychophysical approach to setting limits in manual lifting tasks is discussed in view of experimental procedures used, non-linearity of human perception of load heaviness, and the related experimental outcomes. The results of two studies investigating the human assessment of load acceptability and safety are presented. The first study compares the classical concept of the maximum acceptable weight of lift (MAWL) to the alternative concept of the maximum safe weight of lift (MSWL). The second study utilizes the linguistic magnitude estimation (LME) method to mathematically model human assessment of four categories of lifted loads, including the concepts of acceptable, safe, not-too-heavy, and too-heavy loads for continuous lifting. It is shown that the concepts of the lifted load acceptability and safety are non-linear, and can be modelled with great accuracy using the third degree polynomials. This study also introduces and investigates the concept of the load indifference in assessment of load heaviness, and shows that lack of a cognitive benchmark introduces inconsistency in subjects' perception of load acceptability and safety compared to the concept of too-heavy load for continuous lifting. It is concluded that a new research approach to manual lifting tasks based on cognitive engineering is needed to improve the quality of research methodologies currently utilized in this field. This unexplored area of research should lead to greater understanding of human capacities and limitations in manual lifting tasks in the context of cultural and linguistic anthropology.

Adult↗
PubMed2003

[Quality. A universal story, as old as the hills].

If one were to define Quality today, it would be tempting simply to refer to ISO Norm 9000-2000 where quality is described as the aptitude of the intrinsic characteristics of a product, a system, or a process to satisfy the demands of clients and other interested parties. What is more interesting is to understand how the present notion of quality was fashioned. The process has involved several phases requiring centuries of experience. The idea of checking was first brought forward during an early phase, which ran from the invention of writing to the beginning of the 20th century. This first phase developed slowly and was marked by the invention of measuring instruments and standards. It saw the birth of industrial production which deprived the craftsman of the produced article. The second phase brought forward the notion that checking alone is insufficient. This led to a new concept, Quality Assurance, made possible by the development of mathematical tools (statistics) aimed at controlling the production process. The next phase first appeared in Japan. Faced with the problem of industrial reconstruction after World War II, the Japanese developed a new mode of production management where the two notions of checking and quality assurance were integrated into very concept of the industrial firm. The last phase corresponds to the response of western industry to Japanese competition. Quality is now conceived as a strategic marketing tool playing an essential role in management. Tracing the history of Quality to its origin in ancient times raises the intriguing question as to its profound, possibly archetypic, source.

Drug Industry↗
PubMed1978

An analytical approach to the determination of optimal phasing for external counterpulsation.

An inhomogeneous linear one-dimensional mathematical model is constructed as a conceptual approach to the study of the effects of External Counterpulsation (ECP) on the pressure and flow at the root of the aorta. The optimal operation of ECP is defined by two conditions: (1) minimization of the mean systolic pressure; and (b) maximization of the ratio of diastolic area over systolic area under the total pressure curve. The phase shift of the external pressure is determined so as to satisfy these two requirements. It is demonstrated within our approximation that with a given magnitude of external pressure, the phase shifts that satisfy these two requirements are the same. These phase shifts are linear functions of the systolic fraction of the total cardiac period, and depend on the time for the external wave to travel from the site of application up the vascular bed to the root of the aorta, plus the reflection contributions. Even though these results are derived from a simple model far from the complexity of the actual vasculature, the basic concepts would remain valid even if more complex mathematical treatments would have been used.

Aorta↗
PubMed1985

New prospects in CT image processing via mathematical morphology.

New prospects are foreseen in CT image processing via mathematical morphology (M.M.). M.M. is a set theory based upon the concept of "structuring elements" and allows texture analysis and pattern recognition by performing sequences of neighborhood transformations. This results in a wide range of quantifications. Mathematical morphology applied to CT densitometry allows obtaining the mean density of an organ after its automatic extraction from the background. This operation eliminates the approximations due to the manual selection of the Region of Interest (ROI). Precision, reliability and reproducibility are therefore improved. In this study, we performed the automatic isolation of a sole vertebral body in thoracic or abdominal CT slices to quantify numerous parameters, among them, density of the vertebral trabecular and cortical bones. On scans of the second and third metacarpals, morphomathematical analysis allowed quantification of the parameters of bone evolution: mean cortical density, directional cortico-diaphyseal index, and medullar area. In a different connection, M.M. has allowed automatic segmentation of lung parenchyma, the measurement of its mean density and the determination of the relative importance of the vascular network.

Absorptiometry, Photon↗