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PubMed1990

Quantitative aspects of autocrine regulation in tumors.

Autocrine regulation is defined as a mechanism of self-control in growth and differentiation; this mode of regulation among histologically homologous cells is mediated humorally. Autocrine mechanisms involve: 1. Autonomously controlled production and secretion of autocrine mediators. 2. Distribution of autocrine mediators among cells. 3. Expression by cells of functional receptors for autocrine mediators. 4. Transduction and intracellular integration of signals mediated by autocrine mediators. 5. Growth response. 6. Maintenance of autonomous control of growth and/or differentiation state in the progeny Biochemical and biological evidence for most of these steps in various transformed cells makes it possible to analyze autocrine control as a multifaceted process. This process depends on tumor cellularity and histoarchitecture, on time and on external influences on secretion of autocrine mediators (e.g., estrogens in estrogen-dependent breast cancer). We review the quantitative aspects of experimental evidence for autocrine control in tumors and examine the phenomenological and some mechanistic concepts in creating integrative, quantitative, and experimentally verifiable mathematical models of autocrine regulation.

Breast Neoplasms↗
PubMed1987

[Modeling in chronopharmacology].

The concept of rhythm can be introduced in the mathematic models describing pharmacological phenomena. The modelling can take into account periodic fluctuations in the pharmacokinetic parameters (chronopharmacokinetics), or periodic fluctuations in the susceptibility of an organism to a drug (chronesthesy). It allows to choose the theoretical cases when chronotherapy could be particularly usefull, and also to propose protocols of administration taking into account the time (injection clock-time for example), in the same way that drug amount and route of administration. Modelisation also shows up the complex relationship between a temporally structured organism and an exogenous substance which has not been designed to be integrated into a set of biological rhythms.

Animals↗
PubMed1984

Changes in widowhood and divorce and expected durations of marriage.

A new interpretation of mathematical formulas developed by Keyfitz illustrates how the concept of entropy (H) can be applied to the analysis of marriage dissolution. The quantities H(divorce) and H(widowhood) indicate the changes in marriage duration which would result from small, constant changes in duration-specific divorce and widowhood rates, respectively. An examination of values for the United States, Nepal and Colombia illustrates the utility of H(i) in assessing the impact of changes in widowhood and divorce and clarifies the relationship between H and changes in life expectancy.

Colombia↗
PubMed1983

Frequency-selective adaptation: evidence for channels in the vestibulo-ocular reflex?

The vestibulo-ocular reflex (VOR) is under long-term adaptive regulation to minimize retinal image slip during head movement; normally this process keeps VOR gain (eye velocity divided by head velocity) near 1.0. It has been common to think of the adaptive mechanism as a single pure gain element, although some properties of the system (e.g., frequency-selective changes in the gain of the VOR) argue that it must be more complex. We now report new observations on the frequency selectivity of the adaptive mechanism. Our data suggest a new model in which the VOR operates as a series of parallel, temporal frequency channels, each of which has an independently adjustable gain element. Adaptive changes were produced by oscillating monkeys sinusoidally at a single temporal frequency (0.2 or 2.0 Hz) in visual conditions that cause either increases (toward two) or decreases (toward zero) in VOR gain. When tested in darkness at the adapting frequency, the VOR showed large changes in gain and little or no change in phase. When tested at frequencies other than the adapting frequency, the VOR showed less pronounced changes in gain and unexpected changes in phase. The phase changes were orderly but depended in a complex way on adapting frequency, testing frequency, and VOR gain. We have tested the channels concept by calculating the response properties of a mathematical model that processed its inputs in parallel pathways. The model reproduced our data when we assumed that the vestibular primary afferents were distributed in an orderly way to parallel brain channels that had differing dynamics: vestibular inputs with more phase lead projected to higher frequency channels, which themselves had faster dynamics than their low frequency counterparts. Such an organization, when regulated by an adaptive controller that can selectively alter the gain of one channel, could play a key role in establishing and maintaining the frequency-independent performance seen in the adult VOR.

Adaptation, Physiological↗
PubMedDate not supplied

[Objective evaluation of the aroma and taste of Bulgarian sour milk].

The purpose of the study was to discover the correlation between a subjective organoleptic evaluation of the samples of Bulgarian sour milk and the results of microbiological assays of the amount of and correlations among lactic bacteria, of yeast, and other foreign microflora. A total of 135 samples of milk supplied by different milk factories for tasting were examined. The mean arithmetic value of the percentage of S. thermophilus was found to be different for the samples of sour milk classified with different groups according to the aroma and taste. The data obtained were treated by the passive experimental-statistical method with the use of the REGR program for multiple regression analysis. Based on the theoretical conceptions several experimental models were suggested. The mathematical-statistical treatment allowed the most significant model to be selected for practical use. Control of the adequacy of the suggested models has shown that the model selected may be used for the characteristics of the aroma and taste of Bulgarian sour milk, enabling the tasters to objectively confirm the results of their assessment.

Animals↗
PubMed1981

Infinite experiences, affects and the characteristics of the unconscious.

The work of Matte-Blanco is little understood by psychoanalysts largely because he used mathematical logic as an essential method to elucidate psychoanalytic theory. His findings, however, seem to be important and warrant this simple introductory paper explaining key ideas. Two fundamentally distinct processes, defined as asymmetrical and symmetrical logics are introduced and illustrated. Asymmetrical logic is analogous to secondary process while symmetrical logic has affinity with primary process. Both logic seem to interweave in any thought processes but with asymmetry predominating in scientific thought while symmetrical logic is most evident in psychosis and dreams. It is furthermore argued that the various characteristics of the unconscious, as described by Freud, can be seen as different mental outcomes with symmetrical logic at the base of all of them. A parallel is discovered by Matte-Blanco between the characteristics of symmetrical logic and those of infinite sets as defined mathematically. This leads to an investigation of the concept of infinity and of psychological infinite experiences. These can be readily detected in omnipotence, omniscience, and idealization, but they also seem to occur in extreme emotional states such as being in love, dread and grief. If nuclei of extreme states are contained in any affect, then it is likely that all affects in their cognitive aspects contain experiences of infinity. Symmetrical logic may thus be a common background both to the characteristics of the unconscious and emotionality generally.

Affect↗
PubMed1997

Inference of molecular phylogenetic tree based on minimum model-based complexity method.

In this study, starting with a newly introduced concept of data complexity ("empirical data complexity"), we specify the concept of complexity more concretely in relation to mathematical modeling and introduce "model-based complexity (MBC)". Inductive inference based on the minimum model-based complexity method is then applied to the reconstruction of molecular evolutionary tree from DNA sequences. We find that minimum MBC method has good asymptotic property when DNA sequence lengths approach to infinite and compensates the bias of maximum likelihood method due to the difference of tree topology complexity. The efficiency of minimum MBC method for reconstruction of molecular tree is studied by computer simulation, and results suggest that this method is superior to the traditional maximum likelihood method or its modification by Akaike's AIC.

Animals↗
PubMed2005

Passive and active ventricular elastances of the left ventricle.

BACKGROUND: Description of the heart as a pump has been dominated by models based on elastance and compliance. Here, we are presenting a somewhat new concept of time-varying passive and active elastance. The mathematical basis of time-varying elastance of the ventricle is presented. We have defined elastance in terms of the relationship between ventricular pressure and volume, as: dP = EdV + VdE, where E includes passive (Ep) and active (Ea) elastance. By incorporating this concept in left ventricular (LV) models to simulate filling and systolic phases, we have obtained the time-varying expression for Ea and the LV-volume dependent expression for Ep. METHODS AND RESULTS: Using the patient's catheterization-ventriculogram data, the values of passive and active elastance are computed. Ea is expressed as [formula: see text] Epis represented as: [formula: see text]. Ea is deemed to represent a measure of LV contractility. Hence, Peak dP/dt and ejection fraction (EF) are computed from the monitored data and used as the traditional measures of LV contractility. When our computed peak active elastance (Ea,max) is compared against these traditional indices by linear regression, a high degree of correlation is obtained. As regards Ep, it constitutes a volume-dependent stiffness property of the LV, and is deemed to represent resistance-to-filling. CONCLUSIONS: Passive and active ventricular elastance formulae can be evaluated from a single-beat P-V data by means of a simple-to-apply LV model. The active elastance (Ea) can be used to characterize the ventricle's contractile state, while passive elastance (Ep) can represent a measure of resistance-to-filling.

Blood Pressure↗
PubMed1989

Epidemiological and statistical aspects of the AIDS epidemic: introduction.

In 1988, a government working party studied estimates of incidence and prevalence of numbers of acquired immunodeficiency syndrome (AIDS) cases. They investigated a series of epidemiological, statistical and mathematical problems associated with predicting trends in incidences of AIDS. This paper introduces a series of papers that give a fuller and more technical exposition of the appendixes of that working party report. The papers provide a brief background to the current state of knowledge on the epidemiology of the infection and the disease; a deterministic model for human immunodeficiency virus (HIV) transmission in the male homosexual community in England and Wales is introduced. Back-projection methods are studied in two papers, following the distribution of the incubation period of the disease. The concept of minimum size of the epidemic is introduced. Mathematical functions to describe the spread of HIV infection are refined by using past trends in the incidence of AIDS to estimate values for some parameters. Survival times for AIDS patients from the point of diagnosis are considered and evidence for changes in male homosexual sexual behaviour is studied; lag-time from the point of diagnosis to the report of the case is also examined. There is a comparative analysis of the AIDS epidemic in various European countries. The incubation period of HIV in patients with haemophilia A and B infections and the problems associated with making predictions for different at-risk groups or small subgroups based on geographical area are discussed. Reasons for fluctuation between the number of reported cases from month to month are provided.

Acquired Immunodeficiency Syndrome↗
PubMed1997

Exploring a mixture of distributions using Minitab.

A set of macros has been developed to help the user explore the characteristics of the two-component mixture of distributions. Five distributions are included: normal; exponential; Weibull; lognormal; and uniform. Using the powerful abilities of Minitab (version 9) the user can produce graphs for the conditional and unconditional density, cumulative density, survival and hazard functions. The mean of the unconditional distribution is calculated as the weighted average of the conditional means. A technique is programmed for calculating the unconditional median which cannot be derived mathematically. A What..if..? approach can be helpful in clarifying concepts such as sufficient conditions for unimodality, identifiability of mixtures, and hazard function of mixture of distributions.

Computer Graphics↗
PubMed2006

The concept of normality through history: a didactic review of features related to philosophy, statistics and medicine.

Normality characterises in medicine any possible qualitative or quantitative situation whose absence implies an illness or a state of abnormality. The illness concept was first a philosophical one. But the use of mathematics in the study of biological events, which began with Galton (1822-1911) and with Pearson (1857-1936), changed the frame of reference. In the second part of the 19th century mathematics was used to study the distribution of some biological characteristics in the evolution of the species. Around 1900, statistics became the basis for the study of the diffusion of the illnesses. Half a century later statistics made possible the transition from the description of single cases to groups of cases. Even more important is the concept of "normality" in laboratory medicine. In this field the search for the "perfect norm" was, and possibly still is, under way. The widespread use of statistics in the laboratory has allowed the definition, in a certain sense, of a new normality. This is the reason why the term "reference value" has been introduced. However, even the introduction of this new term has merely shifted the problem, and not resolved it.

Biology↗
PubMed1976

The kinetics of biological phase transitions manifested by sigmoid time curves: a review of approaches.

Experimental biological data showing a time course of sigmoid shape are customarily interpreted in terms of mass-action chemical kinetic theory of reactions in free solution. But the reactive sites in biological systems are often located in solid or structured cellular components through which cooperative interactions may occur, resulting in phase transitions. In inorganic systems, the time course of phase transitions often shows experimental curves of sigmoid shape, and this may be predicted theoretically. Therefore it is suggested that when sigmoid time curves are observed in biological systems containing solid or structured components, mathematical analysis based on cooperative interactions and phase transitions is more likely to be valid than analysis based on mass-action concepts.

Animals↗
PubMed1984

Muscle O2 gradients from hemoglobin to cytochrome: new concepts, new complexities.

The capillary is the principal barrier at high Vo2. Mathematical modelling indicates that at high flow and Vo2 the time required for release of O2 is greater than red cell transit time in some capillaries. This convective shunting appears to be particularly important in the myocardium. The Mb acts to buffer Po2 below 5 Torr during muscle contraction. This greatly increases the transcapillary O2 gradient and promotes O2 delivery. During voluntary movements, Mb should act as a major O2 source in parallel with capillaries. The Kroghian model of the capillary as a "low-resistance" point source of O2 supplying a spatially uniform sink appears to be the reverse of the actual geometry of O2 supply to working red muscle.

Animals↗