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At least 19 recordsLinked to original sources
PubMed1977

Cyclic kinetics and mathematical expression of the primary immune response to soluble antigen. VII. The conveyer hypothesis and its mathematical expression.

The conveyer hypothesis is based on the fact that because of clone predetermination, antibody production takes place in an organism without the presence of antigen as a result of natural cell differentiation. Soluble antigen is an analogue of a specific mitogen which gives rise to reproduction mainly of cells carrying on their surface the immunoglobulin receptors to the given antigen. The mathematical model of the conveyer hypothesis takes into account the initial conditions, among them the background level of antibody-producing cells before injection of a soluble antigen, migration of precursor cells in the draining lymphoid organ, and the rate of precursor differentiation, including the rate of the change of the immunoglobulin receptor number on the cell surface. Changes of antigen concentration in blood determine the intensity of precursor proliferation. Comparison of real experiments (intraperitoneal injections of capsular antigen of Pasteurella pestis into inbred mice) with calculations done on the basis of the developed mathematical model shows a definite qualitative resemblance with the kinetics of antibody-producing cells and free antibodies as well as with the decrease of free antigen concentration in blood. In spite of some differences between model experiments and real experiments the conveyer hypothesis and its mathematical model appear suitable for describing the primary immune response of mice immunized with low doses of capsular antigen of Pasteurella pestis.

Animals↗
PubMed1976

Mathematics and the surgeon.

The surgeon uses elementary mathematics just as much as any other educated layman. In his professional life, however, much of the knowledge and skill on which he relies has had a mathematical strand in its development, possibly woven into the supporting disciplines such as physics, chemistry, biology, and bioengineering. The valves and limitations of mathematical models are examined briefly in the general medical field and particularly in relation to the surgeon. Arithmetic and statistics are usually regarded as the most immediately useful parts of mathematics. Examples are cited, however, of medical postgraduate work which uses other highly advanced mathematical techniques. The place of mathematics in postgraduate and postexperience teaching courses is touched on. The role of a mathematical consultant in the medical team is discussed.

Computers↗
PubMed1978

[Use of mathematics in pathological anatomy].

The author discusses the possibilities of using mathematics in pathological anatomy studies on the basis of data from literature and his own studies. The information on the organization and planning of a mathematical investigation and on the features of the system approach to investigation of pathomorphology problems is presented. The main stages of the mathematical analysis of pathological changes are described with special reference to the use of likelihood and information approaches to the evaluation of the pathology of morphological systems at all levels of the structural organization. The principles of mathematical modelling and axiomatization of pathomorphological processes are outlined. The paper is illustrated with mathematical models of age dynamics of atherosclerosis and informational characteristics of the process of malignization of the stratified squamous epithelium. The general principles of further development of quantitative pathomorphology are briefly discussed.

Adenocarcinoma↗
PubMed1979

Geometric problem solving related to differences in sex and mathematical interests.

Sex differences in Einstellung Effects were confounded by attitudinal factors. Hypothesizing that this was the case for spatial visualization and restructurization, we compared male and female college students' solutions of three elementary geometric problems. Used by Max Wertheimer to study productive thinking, they call for a Gestalt, spatial approach. In group administration to 86 calculus students, males did somewhat better than females, but the reverse held in classes where most women majored in mathematics. Individual administration to 200 Ss, balanced for sex and major, showed that female mathematics majors had more solutions than other females: e.g., 51 percent more compared to 26 percent sex differences. Four hints were available for restructuring each problem. The percentage needing all four hints was highest for male nonmathematics major and next highest for female mathematics majors (e.g., 75 and 23 percent, respectively). Embarrassment at needing hints in such "easy problems" and ego-involvement were factors. Thus, sex differences were less pronounced than differences related to mathematical abilities and interests and to task-and ego-concerns.

Adult↗
PubMed1979

Role of mathematics in cancer research: attitudes and training of Japanese mathematicians.

An extensive survey of attitude towards scientific information of scientists in Japan was conducted in Japan. It was published in a technical report, and this survey is reviewed in this paper, with the hope that this will furnish findings important in working out the plan for promoting exploitation of mathematical talent in biomedical research. Findings are concordant with the impression of foreign visitors: (1) pure mathematicians tend to concentrate on mathematics only; (2) applied mathematics and statistics are heavily oriented toward industry; (3) mathematicians and pharmacologists are very different in their attitudes to scientific information. Based on the personal experience of the author, difficulties to be circumvented in utilizing aptitudes for mathematics and/or statistics in biomedical research are discussed.

Attitude↗
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↗
PubMed1978

Mathematical modeling of lag phases in microbial growth.

This paper describes a mathematical method of the lap phases of Saccharomyces cerevisiae that incorporates the basic concepts previously presented in a two-stage deterministic model for the growth of this organism under conditions of oxygen excess with a sugar as the growth-limiting substrate. The model structure was suggested by an extensive investigation of the causes of the lap phases of S. cerevisiae which found that, in contrast to the traditionally accepted trends, the length of the lap phase was not inoculum-size dependent. This was consistent with other previously published work which suggested that a major factor in the length of the lag phases in S. cerevisiae was the need to synthesize adequate levels of glycolytic and respiratory enzymes. These suggestions were confirmed experimentally with lag-age data. Based on this conclusion a mathematical model was developed incorporating a description of the levels of glycolytic and respiratory enzymes and their effect on the growth rate and metabolism. This model was tested experimentally and the initial results indicate that many aspects of the lag phase of this organism may be described mathematically. The experimental findings further support the concept of primary regulatory control proposed by Bijkerk and Hall.

Glycolysis↗
PubMed1978

[Role of computer technology and mathematical modelling in the treatment of patients after operations on the heart].

On the basis of ten-year experience in theoretical studies and experimental tests mathematical models of hemodynamics were built for the follow-up of parameters of the cardiovascular system which cannot be determined by means of any other modern methods. Three years of clinical studies of the Hewlett-Pachard monitoring computer system and its modification helped to elaborate the mathematical backing, a bank of mathematical models, original automatic programs for measuring the cardiac index, the index of myocardial viability, etc. The automatic system provides for an individual approach in assessing the patient's condition in actual time and for control of the treatment.

Cardiac Surgical Procedures↗
PubMed1978

Comparison of the performance of first-grade and mentally retarded students on the Peabody Mathematics Readiness Test.

The Peabody Mathematics Readiness Test was developed to assess mathematics readiness and identify children who would encounter difficulty in first-grade mathematics. In the present study, we compared performances of mentally retarded subjects and first-grade subjects on this test. Retarded subjects' mean scores were significantly lower than those of the nonretarded subjects on the drawing test; however, there were no significant differences between the mean scores of the groups on the other five subscales.

Adolescent↗
PubMed2025

Mathematical modeling suggests 14-3-3 proteins modulate RAF paradoxical activation.

RAF inhibitor "paradoxical activation" (PA) is a phenomenon where RAF kinase inhibitors increase RAF kinase signaling. Through mathematical modeling and experimental data analysis, we recently demonstrated that the combination of conformational autoinhibition (CA) with the disruption of CA by RAF inhibitors plays an important role in PA. 14-3-3 proteins are known to modulate RAF CA and RAF dimerization. We here extend our mathematical model to include both roles of 14-3-3 proteins, and we derive rigorous analytical expressions of RAF signal regulation as modulated by 14-3-3 proteins. We then use the model to investigate how 14-3-3 proteins may modulate PA. We mathematically show 14-3-3 protein stabilization of the autoinhibited form of RAF should potentiate PA, while 14-3-3 protein stabilization of the active RAF dimer should reduce PA. Our analysis suggests that the net-effect will often be a potentiation of PA, and that 14-3-3 proteins may be capable of inducing PA for RAF inhibitors that normally show little to no PA. We test model-based insights experimentally with two different approaches: forced increases in 14-3-3 expression (which we find amplifies PA) and evolved resistance assays (which suggest increased 14-3-3 expression may contribute to resistance to RAF inhibitors). Overall, this work supports a role for 14-3-3 in modulating RAF-inhibitor mediated paradoxical activation.

14-3-3 Proteins↗
PubMed1979

The prediction of posttraumatic epilepsy. A mathematical approach.

Simple mathematical equations can be used to estimate the probability of posttraumatic seizures. Risk factors and time since the injury are taken into consideration in the calculations. The equations are based on a constant probability model derived from published data. When these formulae are applied to data from a variety of published studies, the predicted incidence of posttraumatic epilepsy based on the mathematical model agrees well with the incidence observed in the study groups.

Brain Injuries↗
PubMed1979

A comparison of mathematical models for estimating right ventricular volumes in animals and man.

Volume of 19 right ventricular canine casts and 11 right ventricular human casts were obtained by water displacement and compared to three different mathematical models for estimating right ventricular volumes by biplane cineangiography. In the canine studies, significant linear correlation coefficients were obtained using the longest measured length method (r = 0.92), the triangular modification of Simpson's rule (r = 0.93), and the elliptical modification of Simpson's rule (r = 0.93). The human studies resulted in similar significant correlation coefficients of 0.96, 0.97, and 0.97, respectively. Although the highest correlation with the lowest standard error of estimate was obtained using the triangular model, all three mathematical models produced volume estimations that feel within acceptabe biological limits of accuracy.

Animals↗
PubMed1978

The evolution of sexual reproduction as a repair mechanism. Part II. Mathematical treatment of the wheel model and its significance for real systems.

The dynamics of populations of self-replicating, hierarchically structured individuals, exposed to accidents which destroy their sub-units, is analyzed mathematically, specifically with regard to the roles of redundancy and sexual repair. The following points emerge from this analysis: 1. A population of individuals with redundant sub-structure has no intrinsic steady-state point; it tends to either zero or infinity depending on a critical accident rate alpha c. 2. Increased redundancy renders populations less accident prone initially, but population decline is steeper if alpha is greater than a fixed value alpha d. 3. Periodic, sexual repair at system-specific intervals prevents continuous decline and stabilizes the population insofar as it will now oscillate between two fixed population levels. 4. The stabilizing sexual interval increases with increased complexity provided this is accompanied by appropriate levels of redundancy. 5. The model closely simulates the dynamics of heterosis effects. 6. Repair fitness is a population fitness: the chance of an individual being repaired is a function of the statistical make-up of the population as a whole at the particular period. Populations living at alpha greater than alpha c either engage in sexual repair at the appropriate time or they die out. 7. The mathematical properties of the model illustrate mechanisms which possibly played a role in the evolution of a mortal soma in relation to sexual reproduction.

Animals↗
PubMed1978

Mathematical optimization of glaucoma visual field screening protocols.

There is potential for significantly shortening the time required for visual field screening protocols by a precise specification of the number, exact location, and sequence of points to be tested. Through statistical and mathematical methods, protocols have been developed for maximizing the probability of detecting at least one visual field defect in a subject who is a risk for early glaucomatous field loss. The mathematical formulation was derived in a generalized manner so that it could be applied to most kinetically or statically determined visual field screening methods.

Glaucoma↗
PubMed1978

Systems-matching by degeneration. II. Interpretation of the generation and degeneration of retinal ganglion cells in the chicken by a mathematical model.

Quantitative data on generation and degeneration of retinal ganglion cells during development (Rager and Rager, 1978) are interpreted in terms of a mathematical model which consists of a system of differential equations. By these equations we attempt to describe the formation of retinal ganglion cells and their termination domains in the tectum. Since ganglion cells seem not to degenerate before their axons have arrived at their termination site and start branching, from the arrival time on they may become competent either to continue to mature or to die. Therefore, to find the actual number of competent cells the extension of the fiber pathway between the retina and the optic tectum had also to be measured and computed. The differential equations are united by the principle that at any given time cells in excess of the number of termination domains have to die. By this model the mathematical function was determined. Several parameter values of this function were optimized with the Gauss-Newton method by which the curve was fitted to the measured values. The high correlation obtained by this method allows to conclude that, to a first approximation, the model may be satisfactory. The evidence of competition for termination sites and of systems-matching by cell death is discussed.

Age Factors↗
PubMed1978

A mathematical model of air and water caloric nystagmus.

A mathematical model is proposed to explain the induction of nystagmic eye movements in response to thermal stimulation of the ear by air and water. Laplace-transformed equations are set up to describe heat flow in the meatus lumen to the ear-drum and heat transmission into meatus wall. Heat transport to the lateral semicircular canal, resulting in convective endolymph flow, and the induction of reflectory eye movements are included in the mathematical description. Input of the model is the time-course of temperature at the irrigating tip, output is the time-course of eye position (in correspondence to experimental nystagmogramms). The predicted nystagmus is in good agreement with experimental results, thus supporting our assumptions on the thermal effects of air and water irrigations.

Air↗
PubMed1979

Evolutionary potential: a mathematical hypothesis of mouse hemoglobin beta chain evolution.

This paper examines the possibility that the linkage arrangements and regulatory properties of genes may be influenced by selection. A mathematical hypothesis is developed in order to show how selective properties of hemoglobin beta chains could have influenced the linkage and regulation of their structural genes. The hypothesis is applied to the case of mouse hemoglobin beta chains. In most mice, closely-linked pairs of loci (doublets) code for two structurally divergent beta chains in unequal amounts. Some mouse strains have singlet alleles, however, coding for another beta chain variant. With the mathematical hypothesis, one can show that selectively determined "evolutionary potentials" may have favored changes in proportions of major and minor chains produced by a doublet allele. In the extreme case, zero production of the minor chain may give a selective advantage, leading to a singlet; conversely, selection may favor linking another gene to the singlet locus to give a doublet. A specific prediction of the model is the stable maintenance under certain conditions of multiple alleles at regulatory loci. The concept of evolutionary potential thus suggests that selection could have influenced the evolution of genotypic fitnesses, in addition to causing changes in gene frequencies as in standard population genetics models

Animals↗