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PubMed1989

A mathematical method for calculating the compensating anterior stop pin setting of a semiadjustable arcon articulator.

The geometry of a semiadjustable arcon articulator and development of mathematical formulae to calculate the setting of the anterior stop pin that compensates for the thickness of the interocclusal centric relation record are discussed. Measurements of the facebow mounted maxillary cast and interocclusal centric relation record are used in these formulae. Testing on 30 diagnostic mountings indicated that the formulae can reliably predict the amount of anterior stop pin opening necessary to allow near parallelism of the maxillary and mandibular bows of the articulator when the interocclusal centric relation record is removed and the mounted casts are brought into occlusion. The vertical component of dental malocclusion is identified as a source of variability in the setting of the anterior stop pin and therefore in the geometry of the articulator; it is defined as a need for further study.

Dental Articulators↗
PubMed1981

The mathematical case against unipolar mania.

A mathematical model is developed based on several assumptions to predict frequency of admission for apparent unipolar mania given that such patients have the same illness as bipolars. The model is compared with data from previous studies of unipolar mania and with data from the author's own study of 77 unipolar manic patients. The observations generally supported the model. It is concluded that the DSM III convention of classifying unipolar manics under the heading "Bipolar disorder" is upheld.

Affective Disorders, Psychotic↗
PubMed1983

A mathematical representation for vessel networks II.

The topographical features of vessel networks can influence the red cell hematocrit, red cell spacing and flow pattern, either directly or indirectly at any level from arteriole to venules. In this article, we continue to treat the mathematical representation for vessel networks. We have treated a vessel segment as a vector quantity and applied this representation to central artery of the gyrus in human brain. The flow mechanism of arteriolar arcades in the bat wing is discussed in this article.

Animals↗
PubMed1989

Mathematical models of tumor growth. IV. Effects of a necrotic core.

Two mathematical models for the control of the growth of a tumor by diffusion of mitotic inhibitor are presented. The inhibitor production rate is taken to be uniform in a necrotic core for the first model and in the nonnecrotic region for the second model. Regions of stable and unstable growth are determined, and conclusions are drawn about the limiting peripheral widths of stable tissue growth for both models. Comparisons of the results from the two models indicate that the models are sensitive to the source distributions of inhibitor production.

Diffusion↗
PubMed1991

Mathematical biology of HIV infections: antigenic variation and diversity threshold.

Infection with the human immunodeficiency virus (HIV) results in severe damage to the immune system and consequent disease (AIDS) after a long and variable incubation period (on average 8-10 years). Why the incubation period should be so long is a puzzle. We outline an explanation based on the dynamics of the interplay between the immune response and antigenic variation in the virus population. The essential idea is that AIDS results when the diversity of antigenic variants of HIV in an infected patient exceeds some threshold, beyond which the immune system can no longer cope. The paper develops a simple mathematical model for this process, based on experimental observations, and explores several ramifications.

Acquired Immunodeficiency Syndrome↗
PubMed1991

A mathematical model for calculating the vector magnetic field of a single muscle fiber.

A mathematical model is described for calculating the volume-conducted magnetic field from active muscle fibers in an anisotropic bundle. With earlier models, the azimuthal magnetic field of a nerve bundle was calculated and the results were compared with the fields measured by toroidal pickup coils. The present model is capable of evaluating all three of the magnetic field components and is thus applicable for analyzing SQUID magnetometer recordings of fields from a muscle bundle. The component of the magnetic field parallel to the fiber axis is more than an order of magnitude smaller than either of the other two components. The amplitude of the magnetic signal is strongly dependent upon the anisotropy of the muscle bundle, the intracellular conductivity, the radius of the muscle fiber, the radius of the muscle bundle, and the location of the fiber in the muscle bundle. The peak-to-peak amplitude of the single-muscle-fiber action field increases linearly with increasing intracellular conductivity, as the square of the radius of the muscle fiber, and exponentially with the distance between the location of the fiber and the center of the bundle.

Action Potentials↗
PubMed1991

Modeling RNA secondary structures. I. Mathematical structural model for predicting RNA secondary structures.

A mathematical model for analyzing the secondary structures of RNA is developed that is based on the connection matrix associated with the planar p-h graph. The classification of the elementary structures allows the introduction of the basis of structural space from which to build the global secondary structure. All admissible solutions belong to the configuration space and can be obtained directly from its basis.

Algorithms↗
PubMed1993

Mathematical modeling of T-cell proliferation.

A mathematical model of the T-lymphocyte proliferation process (in vivo and in vitro) is presented. This model takes into account cell-cycle progression and the regulation by lymphokines (lymphocyte activating factor interleukin 1 and T-cell growth factor interleukin 2). Using data on the generalized picture of the short-term course of viral hepatitis B, the parameter estimation procedure is carried out. The possibility of immunocorrection (by means of injection of a pharmacologic dose of IL-2) during the immune response to viral hepatitis B with T-lymphocyte deficiency is shown.

Animals↗
PubMed1993

Mathematical description and computer simulation of retinal cometlike afterimages: a modified neural equation with stability analysis.

A mathematical model for the spatiotemporal description of a well-known psychophysical phenomenon, the cometlike afterimage effect (CLAIE), is presented. The CLAIE occurs when a bright circular light spot moves slowly in the peripheral human retina. Under these conditions, the leading edge of the dot looks circular, but the trailing edge becomes elongated like a comet's tail whose length increases with speed and luminance, and the illusion is more prominent for photopic backgrounds. This cometlike motion smear is described on the basis of the temporal responsiveness and adaptation of rods. The model is an extension of an existing neural model of M. N. Oğuztöreli et al., with an additional term that allows prolonged saturation and long decay time following exposure to intense stimuli, and these effects are held responsible for the cometlike smear. The model predicts the response of photoreceptors through a nonlinear ordinary integrodifferential equation, which includes known biophysical terms for response dynamics, adaptation, saturation, and kinetics of intermediate components of the phototransduction process. The introduction of a saturation coefficient into the neural equation makes it possible to distinguish the different saturation thresholds of the rod-and-cone system. Numerical determination of the stationary solutions and complete linear stability analysis of the improved neural equation are given for a neuron of second order, and some computational results are presented for phase flows around different singular points in the phase field. A computer simulation based on the improved neural equation is presented for modeling the development and features of the CLAIE as a function of the speed and luminance of the stimulus and the background intensity. The computational results agree well with the psychophysical findings relating to the CLAIE.

Afterimage↗
PubMed1994

DNA damage and the proliferation and aging of cells in culture: a mathematical model with time lag.

This paper is an extension of an earlier one by the same author in which a mathematical model was presented to describe the proliferation and aging of cells in culture. The model consists of a group of ordinary differential equations with a time lag. In the previous paper, the time lag was omitted for simplicity and the resulting differential equations were resolved analytically. It was shown that the model explains the behavior of a cell culture reasonably well. In this paper, the analytical solution of the original differential equations is presented without omitting the time lag. An analytical description of the variations in doubling capability between sister cells that was only simulated numerically in the earlier paper is given.

Animals↗
PubMed1996

Competitive exclusion between axons dependent on a single trophic substance: a mathematical analysis.

A mathematical model is presented of competition between axons for a trophic substance, such as is believed to occur particularly during development. The model is biologically realistic. The growth-stimulating activity of the trophic molecules is assumed to result from their binding to high-affinity receptors on neurons and their axons, but the model also incorporates uptake by nonneuronal cells possessing only lower affinity receptors. Plausible and fairly general assumptions are made concerning the kinetics of binding and internalization and the effects on axonal growth. The model takes into account the possibility that trophic factor production may be regulated by the afferent axons or autoregulated. The variables specified are the "axonal vigor" of each axon, representing the ability of each axon to take up trophic molecules, and the concentration of trophic molecules in the extracellular space of the axonal target region. Of the several parameters introduced, the most important turns out to be the "zero vigor-growth parameter," which is defined as the concentration of trophic molecules that gives zero growth of the vigor of a given axon. By means of a Lyapunov function, it is shown that the system will approach asymptotically to a stable equilibrium characterized by the survival of only the axon whose zero-growth parameter is lowest. Or, if several axons share the same lowest zero-growth parameter, these will all survive. The model may be particularly relevant to the elimination of polyneuronal innervation from developing muscle fibers and from autonomic ganglion cells.

Animals↗
PubMed1990

Mathematical modeling of mass transfer in microvascular wall and interstitial space.

A one-dimensional, unsteady-state mathematical model was developed to describe the transfer of macromolecules across a microvascular wall and into the interstitial space. The proposed theoretical model accounts for both molecular diffusion and convective transfer through the microvascular wall as well as in the interstitial space. The resulting partial differential equations were simultaneously solved using the Laplace transform method. The inversion of the Laplace transformed equations was obtained by using contour integration in the complex region. The final solution is represented by two equations expressing the macromolecule concentration in the microvascular wall region and in the interstitial space, respectively, as functions of time, spatial coordinate, macromolecule concentration in the microvascular wall at the plasma-wall interface, wall thickness, wall-interstitial space equilibrium constant for the macromolecules, ratio of the cross-sectional area of the two regions, sieving coefficients, diffusivity coefficients, and average fluid velocity terms in the two regions. Plots of the macromolecule concentration in both regions as a function of time are presented and discussed for selected values of the parameters. An analytical expression for the total amount of mass which has accumulated in a portion of the interstitial space at any given time was also derived and used to determine the average fluid velocity term and the diffusivity coefficient for each of the two regions from published experimental data (A. Y. Bekker, A. B. Ritter, and W. N. Durán, 1989, Microvasc. Res. 34, 200-216). A numerical nonlinear regression method was used for this purpose. The values for the diffusivity coefficients found in this work for this particular data set compare favorably with the results previously obtained by other workers in similar systems. It is expected that our model will be used in the future to describe the dynamics of mass transfer across a microvascular wall and into the interstitial space, on the basis of the molecular diffusion and/or convective transport mechanisms, thus contributing to the solution of the controversy regarding the nature of the transfer mechanism controlling macromolecule transport in living systems.

Animals↗
PubMed1994

Quantitative structure-activity relationship (QSAR) studies in genetic toxicology: mathematical models and the "biological activity" term of the relationship.

At first sight, the QSAR issue might appear to be a mere pattern recognition problem; however, a purely "surface" approach to QSAR as a pattern recognition problem, not involving the profound plausibility of the solutions, has often been demonstrated to be devoid of scientific value and of predictive strength. The requirement for such a lateral validation should imply the recognition of the basic differences between the two terms of the QSAR issue: biology and chemistry. In particular, the difficulty to derive strong quantitative theories for the biological aspect of QSAR procedures should be taken into serious consideration. Within this conceptual framework, this paper examines the different families of mathematical models (classical regression, multivariate methods, neural networks) used in the QSAR research.

Mathematics↗
PubMed1978

Transfer and dynamics of uric acid in the pregnant rhesus monkey. II. A mathematical model.

The objective of the present study was to develop a mathematical model of the dynamics of uric acid between fetal and maternal compartments in the term pregnant rhesus monkey. In 3 different animals 14C-labeled uric acid was injected into the fetal circulation, the amniotic fluid and the maternal circulation, respectively. In one experiment no uric acid was administered and the fetus was deliberately killed at the beginning of the experiment. Samples of fetal and maternal blood, maternal urine and amniotic fluid were collected at regular intervals. Semilogarithmic time-activity curves were constructed and time constants were determined. An open four-compartment model (fetal-placental plasma, fetal-placental interstitial space, amniotic fluid and maternal plasma) was applied to describe the intercompartmental dynamics of uric acid. Transplacental clearance was approx. 1 ml X min-1 in both directions, maternal renal clearance was about 17 ml X min-1. These results and the calculated values of the other intercompartmental clearances support earlier results, obtained with the steady infusion method. Uric acid concentrations in amniotic fluid and fetal plasma appeared to increase significantly during the experiments. The rise in amniotic fluid levels can only be explained by accepting a yet undefined compartment in which uric acid is produced and cleared directly into the amniotic cavity. It is speculated that this additional compartment could be the fetal lung.

Amniotic Fluid↗
PubMed1991

Mathematical ability and the right-shift theory of handedness.

A genetic theory of handedness, the right-shift theory, associates differential patterns of cerebral functioning with contrasting handedness groups and suggests that individuals with an rs + + genotype will be disadvantaged in mathematical performance. This hypothesis is investigated with contrasting handedness groups drawn from a national sample of over 11,000 children from the National Child Development Study. Some differentiation in cognitive performance between handedness groups is found in the direction predicted by the right-shift theory but the level of the findings is not statistically significant. The rs+ +/mathematical deficit hypothesis is not confirmed.

Achievement↗
PubMed1977

A mathematical expression to describe the ventilatory response to hypoxia and hypercapnia.

A mathematical expression has been developed to describe the ventilatory responses to changes in arterial oxygen saturation (SaO2) and arterial carbon dioxide tension (PCO2). The derivation is based on the experimental observations: (1) that ventilation is a linear function of PCO2 under isoxic conditions, and (2) that ventilation is a linear function of SaO2 under isocapnic conditions. It is assumed that all functions are continuous and single valued, with the implication that for any given SaO2 and PCO2 there is a unique ventilatory response. The analysis following from these three assumptions has enabled us to derive the following expression for ventilation: VI(SaO2, PCO2) = alpha1 - SaO2 - PCO2 + alpha2 - SaO2 + alpha3 - PCO2 + alpha4 where the alpha's are constants for an individual. This equation, which follows uniquely from the assumption stated, is simpler and contains fewer parameters than previous expressions used to describe ventilation.

Humans↗
PubMed1979

A mathematical and graphical analysis of inspiratory muscle action.

In this paper a mathematical and graphical analysis is presented for the action of the diaphragm and the intercostal/accessory muscles of inspiration, in terms of the pressure developed, the volumes displaced and the work performed by each set of muscles. An analogous model is described which behaves according to the analysis. The critical variable by which the action of the diaphragm and intercostal/accessory muscles can be measured is the change in abdominal pressure Pab. When delta Pab = 0 it is assumed that the diaphragm has contracted isometrically and is acting as a fixator preventing an expiratory displacement of the abdomen. When delta Pab greater than 0 the diaphragm shortens and acts as an agonist. When delta Pab less than 0 the diaphragm lengthens as it contracts, performs negative work and the abdomen is displaced in an expiratory direction. For a given change in lung volume, as delta Pab diminishes, there is progressive recruitment of intercostal/accessory muscles and a progressive increase in the work of breathing over and above that required to produce the same change in lung volume by contraction of the diaphragm alone. For values of delta Pab greater than 0 the sum of diaphragm and intercostal/accessory muscle work is less than the total work, because of an increase in the elastic energy stored in the rib cage. For Pab less than 0 there is a decrease in the elastic energy stored in the rib cage leading to a marked increase in work performed and pressures developed by the intercostal/accessory muscles.

Abdomen↗