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At least 595 records · Page 33Linked to original sources
PubMed2002

Optimal range for parvalbumin as relaxing agent in adult cardiac myocytes: gene transfer and mathematical modeling.

Parvalbumin (PV) has recently been shown to increase the relaxation rate when expressed in intact isolated cardiac myocytes via adenovirus gene transfer. We report here a combined experimental and mathematical modeling approach to determine the dose-response and the sarcomere length (SL) shortening-frequency relationship of PV in adult rat cardiac myocytes in primary culture. The dose-response was obtained experimentally by observing the PV-transduced myocytes at different time points after gene transfer. Calcium transients and unloaded mechanical contractions were measured. The results were as follows. At low estimated [PV] (approximately 0.01 mM), contractile parameters were unchanged; at intermediate [PV], relaxation rate of the mechanical contraction and the decay rate of the calcium transient increased with little effects on amplitude; and at high [PV] (approximately 0.1 mM), relaxation rate was further increased, but the amplitudes of the mechanical contraction and the calcium transient were diminished when compared with control myocytes. The SL shortening-frequency relationship exhibited a biphasic response to increasing stimulus frequency in controls (decrease in amplitude and re-lengthening time from 0.2 to 1.0 Hz followed by an increase in these parameters from 2.0 to 4.0 Hz). The effect of PV was to flatten this frequency response. This flattening effect was partly explained by a reduction in the variation in fractional binding of PV to calcium during beats at high frequency. In conclusion, experimental results and mathematical modeling indicate that there is an optimal PV range for which relaxation rate is increased with little effect on contractile amplitude and that PV effectiveness decreases as the stimulus frequency increases.

Animals↗
PubMed1967

Cell growth and division. I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures.

A mathematical model is formulated for the development of a population of cells in which the individual members may grow and divide or die. A given cell is characterized by its age and volume, and these parameters are assumed to determine the rate of volume growth and the probability per unit time of division or death. The initial value problem is formulated, and it is shown that if cell growth rate is proportional to cell volume, then the volume distribution will not converge to a time-invariant shape without an added dispersive mechanism. Mathematical simplications which are possible for the special case of populations in the exponential phase or in the steady state are considered in some detail. Experimental volume distributions of mammalian cells in exponentially growing suspension cultures are analyzed, and growth rates and division probabilities are deduced. It is concluded that the cell volume growth rate is approximately proportional to cell volume and that the division probability increases with volume above a critical threshold. The effects on volume distribution of division into daughter cells of unequal volumes are examined in computer models.

Animals↗
PubMed1996

Role of erythrocytes in leukocyte-endothelial interactions: mathematical model and experimental validation.

The binding of circulating cells to the vascular wall is a central process in inflammation, metastasis, and therapeutic cell delivery. Previous in vitro studies have identified the adhesion molecules on various circulating cells and the endothelium that govern the process under static conditions. Other studies have attempted to simulate in vivo conditions by subjecting adherent cells to shear stress as they interact with the endothelial cells in vitro. These experiments are generally performed with the cells suspended in Newtonian solutions. However, in vivo conditions are more complex because of the non-Newtonian flow of blood, which is a suspension consisting of 20-40% erythrocytes by volume. The forces imparted by the erythrocytes in the flow can contribute to the process of cell adhesion. A number of experimental and theoretical studies have suggested that the rheology of blood can influence the binding of circulating leukocytes by increasing the normal and axial forces on leukocytes or the frequency of their collision with the vessel wall, but there have been no systematic investigations of these phenomena to date. The present study quantifies the contribution of red blood cells (RBCs) in cell capture and adhesion to endothelial monolayers using a combination of mathematical modeling and in vitro studies. Mathematical modeling of the flow experiments suggested a physical mechanism involving RBC-induced leukocyte dispersion and/or increased normal adhesive contact. Flow chamber studies performed with and without RBCs in the suspending medium showed increases in wall collision and binding frequencies, and a decrease in rolling velocity in the presence of erythrocytes. Increased fluid viscosity alone did not influence the binding frequency, and the differences could not be attributed to large near-wall excesses of the lymphocytes. The results indicate that RBCs aid in the transport and initial engagement of lymphocytes to the vascular wall, modifying the existing paradigm for immune cell surveillance of the vascular endothelium by adding the erythrocyte as an essential contributor to this process.

Biophysical Phenomena↗
PubMed1998

Mathematical modeling and fluorescence imaging to study the Ca2+ turnover in skinned muscle fibers.

A mathematical model was developed for the simulation of the spatial and temporal time course of Ca2+ ion movement in caffeine-induced calcium transients of chemically skinned muscle fiber preparations. Our model assumes cylindrical symmetry and quantifies the radial profile of Ca2+ ion concentration by solving the diffusion equations for Ca2+ ions and various mobile buffers, and the rate equations for Ca2+ buffering (mobile and immobile buffers) and for the release and reuptake of Ca2+ ions by the sarcoplasmic reticulum (SR), with a finite-difference algorithm. The results of the model are compared with caffeine-induced spatial Ca2+ transients obtained from saponin skinned murine fast-twitch fibers by fluorescence photometry and imaging measurements using the ratiometric dye Fura-2. The combination of mathematical modeling and digital image analysis provides a tool for the quantitative description of the total Ca2+ turnover and the different contributions of all interacting processes to the overall Ca2+ transient in skinned muscle fibers. It should thereby strongly improve the usage of skinned fibers as quantitative assay systems for many parameters of the SR and the contractile apparatus helping also to bridge the gap to the intact muscle fiber.

Animals↗
PubMed1994

Concurrent finger-tapping in mathematically gifted males: evidence for enhanced right hemisphere involvement during linguistic processing.

O'Boyle and Benbow (1990) have suggested that enhanced involvement of the right hemisphere (RH) during basic information processing is a neuropsychologic characteristic of the gifted brain. To provide converging evidence for this hypothesis, the present study was conducted using a concurrent finger-tapping paradigm. Specifically, 24 mathematically precocious and 16 average ability adolescent males were required to tap a key as quickly as possible while sitting silently (baseline condition), concurrently reading a paragraph aloud (verbal load), or encoding a random form into memory (spatial load). For average ability subjects, the concurrent verbal load reduced tapping rate for the right but not the left hand, reflecting a division of LH resources between linguistic processing of the paragraph and motor control of the contralateral hand. In contrast, for gifted subjects, both their left- and right-hand tapping rates were significantly reduced, suggesting that both hemispheres were engaged during verbal processing. The concurrent spatial task produced a small but reliable reduction in finger-tapping rate for both the left and right hand in each group. These findings provide additional support for the notion that enhanced reliance on RH functioning is a physiological correlate of mathematical precocity in gifted males.

Adolescent↗
PubMed1999

Mathematical relationships between uterine contractions, cervical dilatation, descent and rotation in spontaneous vertex deliveries.

OBJECTIVE: To determine the mathematical relationships between the strength and duration of the uterine contractions, the descent and rotation of the fetal head and the degree of cervical dilatation in 50 multiparous women with spontaneous vaginal deliveries using a simple device applied to the fetal vertex. METHOD: A simple device for monitoring the progress of labor was applied to the fetal vertex. The device allows the continuous monitoring of descent and rotation of the fetal head. The amount of descent and the degree of rotation were also determined by repeated vaginal examinations as well as the degree of cervical dilatation. The frequency of uterine contractions was also recorded on a partogram. RESULT: A good correlation was found between the amount of descent of the fetal vertex (r = 0.975) and between the degree of rotation of the fetal head (0.83) determined by both methods. Multiple regression analysis was then performed and the degree of cervical dilatation in cm at any given time during the first stage of labor was found to be equal to 2.859 + 0.583 fetal head station in (cm) + 0.1983 internal rotation in degrees -0.0493 (station x internal rotation) + 0.1599 station2 + 0.3622 uterine contractions per 10 min. A nomogram was constructed allowing the calculation of cervical dilatation for a given station of the head, degree of rotation and frequency of uterine contractions. CONCLUSION: There is a defined mathematical relationship between the degree of descent and rotation of the fetal head, the degree of cervical dilatation and the frequency of uterine contractions in multiparous women with vertex presentation. The first three variables can be continuously determined by using the described device. Incorporation of the device into a reusable fetal scalp electrode allows the dual mechanical and electronic monitoring during labor with minimal vaginal examinations.

Cervix Uteri↗
PubMed1997

A mathematical approximation for the solution of a static indentation test.

The classical contact problem of the indentation of a thin compressible linear elastic layer bonded to a rigid substrate is considered. Closed-form mathematical approximations of the deformation are presented for the cases of plane indentation by a rectangular block and three dimensional indentation by a plane-ended (axisymmetric) cylinder. The approximations are analyzed in the context of a static indentation test by comparison of applied load values to those obtained using a classical integral transform solution. In the case of plane indentation, the mathematical and classical predictions agree to within 2% relative error for aspect ratios between 0.1 and 1.0 and apparent Poisson ratio between 0.0 and 0.3. Comparisons for the axisymmetric case indicate a similar pattern. The main advantage of the new approach is that it yields closed-form approximations of the static indentation solution which can also capture the essential singular behavior.

Animals↗
PubMed2003

Use of the mathematical principle of inversion in young children.

An important issue in the development of mathematical cognition is the extent to which children use and understand fundamental mathematical concepts. We examined whether young children successfully use the principle of inversion and, if so, whether they do so based on qualitative identity, length, or quantity. Twenty-four preschool children and 24 children in Grade 1 were presented with three-term inversion problems (e.g., 3+2-2) and standard problems of similar magnitude (e.g., 2+4-3). Problems were presented in three conditions to determine whether children used inversion at all and, if so, whether their decisions were based on quantitative or nonquantitative features of the problems. Both preschool and Grade 1 children showed evidence of using inversion in a fully quantitative manner, indicating that this principle is available in some form prior to extensive formal instruction in arithmetic.

Child↗
PubMed1991

Mathematical model of cellular basis for the respiratory sinus arrhythmia.

The respiratory sinus arrhythmia (RSA) is a vagally mediated oscillation in cardiac cycle length at the frequency of breathing. We developed a mathematical model that predicted the temporal and frequency dependence of the RSA. We used the mathematical model to examine the underlying cellular basis for the RSA at the level of the sinus node. We alternated efferent vagal activity between a low and a high frequency at the frequency of breathing. This oscillation caused the rate of acetylcholine (ACh) release to oscillate between a low and a high rate at the frequency of breathing. ACh degradation followed linear pharmacokinetics for physiological concentrations of ACh. Therefore, the concentration of ACh in neuroeffector junctions of the sinus node oscillated at the frequency of breathing. Membrane potential responded rapidly to changes in the concentration of ACh relative to the rate of ACh degradation. Thus, the time course of the RSA depended on the rate of ACh degradation. Membrane potential oscillated at several integer multiples of frequency of breathing and at various higher frequencies, which were integer multiples of the frequency of breathing and the frequencies of firing of the sinus node. However, computing cardiac cycle length from membrane potential eliminated the higher frequencies. Therefore, cardiac cycle length oscillated at several integer multiples of the frequency of breathing, but not at these higher frequencies.

Acetylcholine↗
PubMed1991

Unequal cell division, growth regulation and colony size of mammalian cells: a mathematical model and analysis of experimental data.

This work describes mathematically the dynamics of expansion of cell populations from the initial division of single cells to colonies of several hundred cells. This stage of population growth is strongly influenced by stochastic (random) elements including, among others, cell death and quiescence. This results in a wide distribution of colony sizes. Experimental observations of the NIH3T3 cell line as well as for the NIH3T3 cell line transformed with the ras oncogene were obtained for this study. They include the number of cells in 4-day-old colonies initiated from single cells and measurements of sizes of sister cells after division, recorded in the 4-day-old colonies. The sister cell sizes were recorded in a way which enabled investigation of their interdependence. We developed a mathematical model which includes cell growth and unequal cell division, with three possible outcomes of each cell division: continued cell growth and division, quiescence, and cell death. The model is successful in reproducing experimental observations. It provides good fits to colony size distributions for both NIH3T3 mouse fibroblast cells and the same cells transformed with the rasEJ human cancer gene. The difference in colony size distributions could be fitted by assuming similar cell lifetimes (12-13 hr) and similar probabilities of cell death (q = 0.15), but using different probabilities of quiescence, r = 0 for the ras oncogene transformed cells and r = 0.1 for the non-transformed cells. The model also reproduces the evolution of distributions of sizes of cells in colonies, from a single founder cell of any specified size to the stable limit distribution after eight to ten cell divisions. Application of the model explains in what way both random events and deterministic control mechanisms strongly influence cell proliferation at early stages in the expansion of colonies.

Animals↗
PubMed1984

A mathematical model that applies to protein degradation and post-translational processing of proteins and to analogous processes for other molecules in non-growing and exponentially growing cells.

A mathematical model is presented that describes first order degradation and post-translational processing of proteins in non-growing and exponentially growing cells. The model applies to proteins that are substrates or products of processing. General equations are presented that can be applied to many different experimental protocols. Application of the model to pulse-chase and continuous labeling experiments is illustrated. The mathematical expressions apply to any cellular component that is synthesized in proportion to cellular mass and is degraded or processed by reactions that follow first order kinetics. However, in this paper, the model is discussed solely as it applies to protein metabolism.

Amino Acids↗
PubMed1987

A mathematical model for determining minimal inhibitory concentrations (MICs) via diffusion assays.

A mathematical model is presented for the description of inhibition zones in a diffusion bioassay. In such an experiment the drug is placed at the center of a Petri dish containing a bacterial lawn in an agar gel and after a certain incubation period one observes a concentric ring around the center marking the toxic area. From the knowledge of the radius rtox of the toxic zone, the lower limit ctox at which the inhibitory response is observed can be readily calculated. This quantity is very important in evaluating the sensitivity of microorganisms to toxic substances. The mathematical model of the assay is given by a two-dimensional diffusion equation describing the changes in drug concentration due to diffusion, decay of the chemical and consumption by bacteria. The diffusion equation being mildly non-linear is solved numerically with the aid of a computer. For this purpose a numerical solver was developed as well as a "best-fit" simulation program that fits the parameters for which experimental values could not be obtained. The method was tested with N-methyl-N'-nitro-N-nitrosoguanidine and ethylmethanesulfonate and was seen to be fast, efficient, and inexpensive. In principle it could be used for routine quantitative screening for toxicity of chemicals.

Diffusion↗
PubMed1989

A mathematical model of the gate control theory of pain.

The first test which any theory of pain must pass is that it must be able to explain the phenomena observed in acute pain in humans. This criterion is used to test the major theory of pain at present, the gate control theory of Melzack & Wall (1965, 1982). The theory is explicit enough to be cast in mathematical terms, and the mathematical model is shown to explain the observations considered. It also points up a common misconception on the consequences of the theory, and thus demolishes an argument which has been used against it. A hypothesis of the origin of rhythmic pain is then made, and consequent testable predictions given. This is the first time that the gate control theory has been used to explain any quality of pain. It has important consequences for the treatment of such pain. Finally, the applicability of the gate control theory as an explanation for chronic pain is discussed.

Humans↗
PubMed1989

A mathematical model of the kinetics of blood coagulation.

Linear mathematical models of the kinetics of blood coagulation have previously been presented (Levine, 1966, Science, N.Y. 152, 651; Martorana & Moro, 1974, Math. Biosci. 21, 77). In this paper a non-linear mathematical model of the extrinsic pathway of blood coagulation is presented to take into account a positive feedback. The feedback is due to factor Va as a co-factor involved in thrombin formation. The extrinsic pathway is shown to function as an amplifier cascade if a vessel wall injury exceeds a threshold value. For sub-threshold stimulation, the extrinsic pathway does not function.

Blood Coagulation↗
PubMed1998

A mathematical model of drug resistance: heterogeneous tumors.

A mathematical model is developed to describe the growth and control of a heterogeneous tumor. The main aspect of the model is that it takes into account induced drug resistance. The mathematical model is a system of two ordinary differential equations that describes the growth of the cancer along with the effects of chemotherapy. The model is analyzed to determine what some of the critical parameters are; how we determine an effective treatment; how combination chemotherapy should be delivered; and how this model may help us develop more effective cancer chemotherapeutic treatments.

Animals↗
PubMed2003

Number and measure: Hermann von Helmholtz at the crossroads of mathematics, physics, and psychology.

In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics (Grassmann/Du Bois), on the possibility of quantitative psychology (Fechner/Kries, Wundt/Zeller), and on the meaning of temperature measurement (Maxwell,Mach.). Late nineteenth-century scrutinisers of the foundations of mathematics (Dedekind, Cantor, Frege, Russell) made little of Helmholtz's essay. Yet it inspired two mathematicians with an eye on physics (Poincaré and Hölder), and a few philosopher-physicists (Mach, Duhem,Campbell). The aim of the present paper is to situate Helmholtz's contribution in this complex array of nineteenth-century philosophies of number, quantity, and measurement.

Germany↗
PubMed1995

A mathematically based classification of root canal curvatures on natural human teeth.

Testing of root canal-shaping instruments on natural human teeth has many difficulties, because of the different anatomical forms of root canals. There is a lack of an internationally accepted and mathematically based classification of root canal morphology. The aim of this study was to give a mathematical description of root canal forms with the help of differentiated geometrical pattern analysis and computer graphics. The measurements of 433 roots were conducted on isometric radiographs taken from the clinical view. Measured points of the same radiographs were approximated using fourth degree polynomial functions describing the imaginary axis of canals. The classification of root canal morphology on the basis of Schneider's angle differs from the classification of geometrical pattern analysis. Fourth-degree function approximation as a new method for the description of the shape of root canal curvatures seems to be exact and reliably repeatable. This type of classification of root canals is suitable for standardizing test specimens, including natural human teeth used for testing root forms: I (straight), J (apical curve), C (entirely curved), or S (multicurved).

Chi-Square Distribution↗
PubMed2001

Mathematical model of a hybrid dispersed network-membrane-based controlled release system.

A mathematical model with an exact solution is presented for the controlled release of a drug from a hybrid dispersed network-membrane based system. Both hollow fiber and flat membrane device geometries are considered. The reservoir is loaded with a drug dispersed in a liquid phase. This reservoir is bounded by a microporous membrane, the pores of which are filled with liquid immiscible with the reservoir phase liquid. The drug dissolves from the solid network into the reservoir liquid and migrates through the reservoir toward the microporous membrane. At the interface between the reservoir and the pore, the solute partitions between the reservoir and the pore liquid phases, before diffusing outward through the membrane pore. Experimental results are in close agreement with the release profiles predicted by the mathematical model. Parametric studies reveal the interaction between system parameters and the controlled release behavior. The presence of a dispersed drug phase in the reservoir results in the release of drug for an extended time. The release rate of the drug may be controlled by its rate of diffusion through the membrane pores or by its rate of dissolution into the reservoir liquid.

Chemistry, Pharmaceutical↗