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PubMed2005

Kt/V and nPNA in pediatric peritoneal dialysis: a clinical or a mathematical association?

The relationship between dialysis dose and nutrition is a field of particular interest in chronic pediatric dialysis (PD), and a positive correlation between ureaKt/V and nPNA has been published, suggesting a better nutritional status is associated with higher dialysis doses. However, this relationship has also been criticized as being the result of a mathematical coupling resulting from the same variables. The objective of the study was to establish the relationship between dialysis dose (Kt/V) and nutritional variables: daily protein intake (DPI), protein catabolic rate (PCR), protein equivalent of total nitrogen appearance (PNA) and nitrogen balance (NB) in dialyzed children. A cohort, prospective, observational study was carried out, for which 223 biochemical measurements were performed in 20 patients, ages 1 month to 14.3 years old (13 males), under PD for a 12-month period of follow-up. Monthly residual and total ureaKt/V, DPI, PCR, nPNA and NB were calculated, and the correlation between Kt/V and the nutritional parameters was evaluated. The Borah equation was used to calculate the nPNA. The data are reported as the mean plus or minus the standard error. All statistical comparisons were done with a paired t test, and two-way ANOVA for repeated measures was used to calculate correlations. A P <0.05 was considered significant. Mean total and residual Kt/V was 3.4+/-1.3 and 1.69+/-1.27, respectively; nPNA and PCR were 1.38+/-0.44 and 1.39+/-0.43 g/kg/day, daily protein intake (DPI) was 3.25+/-1.27 g/kg/day, and NB showed a value of 1.86+/-1.25 g/kg/day. A significant positive correlation was found between Kt/V and DPI, PCR, DPC and nPNA (all values P <0.0001), but no correlation was found between total and residual Kt/V vs. nitrogen balance ( P:ns). Total Kt/V showed a significant positive correlation with nPNA, but it did not show any correlation with nitrogen balance, suggesting that the relationship with nPNA is the result of a mathematical association calculated from the same variables.

Adolescent↗
PubMed2006

Gaining insights into human viral diseases through mathematics.

Mathematical models have been recognized as powerful tools for providing new insights into the understanding of viral dynamics of human diseases at both the population and cellular levels. This article briefly reviews the role of mathematical models and their historical precedents for creating new knowledge of the mechanisms of disease pathogenesis, transmission, and control of some human viral infections. Future research in the modelling of infectious diseases will need to rely upon incorporation of the fundamental principles that govern viral dynamics in vivo as well as in the population.

Humans↗
PubMed1987

A mathematical description of the comminution of food during mastication in man.

Chewing performance was quantified by determining the particle-size distribution of comminuted food as a function of the number of chewing strokes. The rate of food breakdown was taken to be the result of a combined selection and breakage process; this was quantified in a mathematical model. A linear operation on the particle-size distribution described the changes in this distribution that resulted from an additional chewing stroke. Detailed information was obtained from eight subjects on the selection and breakdown of food particles of different sizes. There were considerable inter-individual differences in the selection chances for small particles. The mathematical method facilitates study of the influence of dental morphology and muscle-related factors on the comminution of food particles.

Adult↗
PubMed1988

Mathematical and descriptive classification of variations in dental arch shape in an Australian aborigine population.

The ability to describe dental arch shape is necessary for biomechanical studies of occlusion as well as for anthropological studies of human and primate dental variation. A mathematical method of describing and classifying human dental arch shape was used to assess the nature of individual variability. The method involved the calculation of a series of third-degree polynomials which were fitted to coordinate points along the dental arcade. The slopes of the polynomials, evaluated at these coordinate points, provided a multivariate description of shape, independent of arch size. Graphic representations of arch shape could be constructed from the polynomial equations. These mathematical techniques were used in association with multivariate and univariate statistics to explore the types of variability in dental arch shape among a population of Australian aborigines. The results illustrated the ambiguities of conventional subjective classifications.

Adult↗
PubMed1992

Mathematical models for the cellular concentrations of cyclin and MPF.

Several mathematical models have been proposed for regulation of the cell cycle in early embryos by cyclin and maturation-promoting factor (MPF). In this paper the previously proposed models for cyclin and MPF activity are analyzed, and the validity of those models based on the mathematical behavior of their solutions and on physical considerations are discussed. In addition, three further models are proposed that exhibit the periodic behavior necessary for modeling the mitotic clock but that do not have certain of the limitations of the other models.

Animals↗
PubMed1984

Selective effects of secretagogues on insulin secretion: a mathematical model.

A mathematical model of the secretion of insulin from pancreatic islets of Langerhans is proposed. Previously proposed mathematical models of insulin secretion have dealt solely with glucose-stimulated release, and not with the more complex patterns of secretion (such as "off-responses") in response to other secretagogues or combinations of secretagogues. We conclude that an off-response is consistent with a compartmental model; and the facilitating effect of a constant concentration of glucose on leucine-stimulated insulin secretion is consistent with a selective effect of glucose on a single compartment of the model.

Animals↗
PubMed1983

Mathematical model of the human ankle joint.

It has been suspected that the mechanical environment in which a particular joint functions has an effect on the initiation or progression of degenerative joint disease. The objective of this study is to define the mechanical environment of the ankle joint, specifically, the contact areas and pressure distributions, through the development and analysis of a simplified mathematical model. Since the state of pressure across articular surfaces during function is influenced by joint incongruity, cartilage thickness profile and the geometry of the opposing surfaces, these factors have been incorporated into the model formulation. Mathematical analysis of the model has resulted in pressure distributions in both the anterior-posterior and medial-lateral directions and contact area growth plots which correlate well with observed ankle contact patterns obtained from in vitro investigations. The significance of joint incongruity to these pressure distributions and to the relative immunity of the ankle joint to primary osteoarthritis is discussed.

Ankle Joint↗
PubMed1991

Three-dimensional mathematical model analysis of the patellofemoral joint.

This paper is concerned with a mathematical model analysis of the patellofemoral joint in the human knee, taking into account the articular surface geometry and mechanical properties of the ligament. It was made by the application of a computer-aided design theory (previously studied) and it was possible to express the articular surface geometries in a mathematical formulation and hence elucidate the joint movement mechanics. This method was then applied to a three-dimensional geometrical model of the patellofemoral joint. For the modelling of tendofemoral contact at large angles of knee flexion, the geodestic line theory was adopted. Applying the Newton-Raphson method and the Runge-Kutta Gil method to the model, variables such as patellar attitudes, patellofemoral contact force and tensile force of the patellar ligament for various knee flexion angles were computed. Applying the Hertzian elastic theory, contact stress was also computed. These results showed good agreement with the previously reported experimental results. As an application for the model, some parameter analyses were performed in terms of the contact stress variations and compared with those of the normal knee. The simulation results indicated that both the Q-angle increase and decrease increased contact stress, the patella alta showed undulating variations of stress while the patella infera showed little change of stress, and the tibial tuberositas elevation showed 20-30% reduction of stress.

Aged↗
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

Mathematical considerations of competitive polymerase chain reaction.

Reverse transcriptase polymerase chain reaction (PCR) is used frequently to monitor gene expression. It is generally regarded as a qualitative technique, although refinements have been made to improve quantification. The object of this study was to develop competitive PCRs to allow reliable quantification of the rat T cell cytokines interferon-gamma (IFN-gamma), interleukin-2 (IL-2) and interleukin-4 (IL-4). Truncated constructs of cDNA for these cytokines were prepared using appropriate pairs of standard and specially constructed primers designed to allow subsequent co-amplification of the purified competitor construct and the target cDNA. A high resolution capillary electrophoresis (CE) system was used for PCR product detection. The performance of the system was compared with a mathematical model that describes and predicts the exponential nature of the PCR reaction. Co-amplification of the competitor and target were achieved. A high level of resolution and accuracy was achieved using CE to detect and quantify the PCR products. The rates of generation of the respective products conformed closely but not exactly to the predictions of the mathematical model. The competitive PCRs estimated initial numbers of target cDNA within 1.1-5.0-fold relative to the amount of starting material as assessed by conventional spectrophotometric absorbance prior to dilution and amplification. A convenient and flexible competitive PCR strategy has been developed with accurate resolution of products and reliable quantification. Assay variability was far less than biological variability likely to be encountered in experiments investigating immunological responses in rats or other animals.

Animals↗
PubMed1991

The observed form of coated vesicles and a mathematical covering problem.

A connection is made between (1) the observed structures of clathrin cages and (2) the mathematical problem of determination of the smallest diameter of n equal circles by which the surface of a sphere can be covered without gaps. For different numbers n of circles, it is found that the various clathrin polyhedra identified so far provide topologically the same configurations as the proven solutions of the sphere-covering problem for some n or improve on the currently best conjectured solutions for other n. Thus a study of some biological structures has, in this case, given additional insight into a mathematical problem.

Clathrin↗
PubMed1992

Mathematical characterization of Chaos Game Representation. New algorithms for nucleotide sequence analysis.

Chaos Game Representation (CGR) can recognize patterns in the nucleotide sequences, obtained from databases, of a class of genes using the techniques of fractal structures and by considering DNA sequences as strings composed of four units, G, A, T and C. Such recognition of patterns relies only on visual identification and no mathematical characterization of CGR is known. The present report describes two algorithms that can predict the presence or absence of a stretch of nucleotides in any gene family. The first algorithm can be used to generate DNA sequences represented by any point in the CGR. The second algorithm can simulate known CGR patterns for different gene families by setting the probabilities of occurrence of different di- or trinucleotides by a trial and error process using some guidelines and approximate rules-of-thumb. The validity of the second algorithm has been tested by simulating sequences that can mimic the CGRs of vertebrate non-oncogenes, proto-oncogenes and oncogenes. These algorithms can provide a mathematical basis of the CGR patterns obtained using nucleotide sequences from databases.

Algorithms↗
PubMed1976

A mathematical model of cerebrospinal fluid dynamics.

The ability to solve systems of simultaneous non-linear differential equations by a combination of analytical and computational techniques has encouraged the development of valid mathematical models of biological phenomena. The dynamics of the cerebrospinal fluid (CSF) system has been the subject of closer scrutiny in recent years since the recognition of symptomatic low-pressure hydrocephalic states in man. A mathematical model has been derived from 7 assumptions: (1) That the brain is a spherical shell. (2) That CSF is secreted at a constant rate. (3) That CSF absorption is linearly dependent on pressure. (4) That flow between the CSF compartments is proportional to the pressure difference. (5) That Laplace's Law holds for the visco-elastic properties of the brain. (6) That there is compliance in the spinal compartment of the CSF system. (7) That vascular pulsations in the cranial and spinal compartments are capacitatively coupled. Using known data (and estimates of as yet unknown values) for the several parameters, the validity of the model has been successfully tested against 3 clinical conditions. This model extends our understanding of derangements of CSF dynamics and suggest where further research may yield data at present lacking.

Cerebrospinal Fluid↗
PubMed1983

Mathematical immunogenetics II. Antibody incidence structure.

Mathematical Immunogenetics I argued for the development of mathematics as a language for immunogenetics. A three-fold factorization of a reaction matrix was seen to be the important form of a model of a first order immunogenetic system. In the present paper, results of the authors on determining this factorization are reworked from a physical perspective and presented in an algorithmic form that can be used to compute a labeling matrix from data. Computer programs to perform these computations are in preparation.

Animals↗
PubMed1994

Weber's law modeled by the mathematical description of a beam balance.

A beam balance is analyzed as a model that describes Weber's law. The mathematical derivations of the torques on a beam balance produce a description that is strictly compatible with that law. The natural relationship of the beam balance model to Weber's law provides for an intuitive understanding of the relationship of Weber's law to sensory and receptor systems. Additionally, this model may offer a simple way to compute perturbations that result from unequal effects on coupled steady-state systems. A practical outgrowth from this work is that a relatively simple mathematical description models sensory phenomena and may aid in the understanding of sensory and receptor systems.

Humans↗
PubMed1993

Bridge-building between mathematical theory and molecular biology: the REV2 gene as paradigm.

The DNA damage-repair theory of R.H. Haynes anticipated the possibility of dose-dependent repair processes. The mathematical formalism developed by Haynes and coworkers on the basis of this theory provided tools to probe for the existence of inducible components of mutation or recombination by analysis of dose-response curves. Subsequently, we found that biological and molecular analysis of the Saccharomyces cerevisiae REV2 gene supported the validity of the postulates derived from the mathematical analysis. In this article, we briefly review the foregoing and summarize evidence that the REV2 gene product might function in DNA damage-inducible repair and mutation processes.

Amino Acid Sequence↗
PubMed1995

Mathematics of three-dimensional eye rotations.

The recording of three-dimensional eye position has become the accepted standard in oculomotor research. In this paper we review the mathematics underlying the representation of three-dimensional eye movements. Rotation matrices, rotation vectors and quaternions are presented, and their relations described. The connection between search coils and rotation matrices is explained, as well as the connection between eye position and eye velocity. While examples of applications of the formulas to vestibulo-ocular research are given, the methods and mathematical analyses are also useful for studying other motor systems.

Eye Movements↗
PubMed1993

A mathematical model of the effect of aging on bone marrow cells colonizing the thymus.

The process of T cell generation in the thymus involves complex cell-cell interactions between the various types of thymic stromal cells, thymocyte progenitors, thymocytes at different stages of differentiation and external factors. We applied the tool of mathematical modelling to analyze hypotheses and direct experiments concerning mechanisms underlying the observed developmental inferiority of bone-marrow thymocyte progenitors from old mice. Previous experimental data showed that lower cell numbers were obtained from old bone marrow-derived thymocyte progenitors, compared to young bone marrow-derived progenitors, when colonizing simultaneously the same fetal thymus. In this study, simulations based on the mathematical model indicate that the developmental inferiority of old bone marrow-derived progenitors cannot be explained by a change in a single parameter, such as the observed differences in progenitor frequency, an increase in cell cycle duration, a reduction in the fraction of proliferating cells in old age, and/or an increase in the rate of cell death. We have performed experimental measurements of the fractions of cycling cells. No significant difference was found between these fractions in young and old bone marrow-derived thymocytes. The difference in developmental patterns of young and old bone marrow-derived thymocytes may be due to a combination of more than one mechanism, possibly including interactions between competing thymocytes of old and young bone marrow origin.

Aging↗