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PubMed1980

Determinants of distortions in CO2 catheter sampling systems: a mathematical model.

A mathematical model was developed to predict the distortions in the measured expiratory CO2 concentration time profile caused by catheter sampling systems. Parameters considered included the expiratory flow and concentration profiles, the sample flow rate, the sample tube dimensions and the sample cell volume. Unless care is taken in choosing the parameters of a catheter sampling system, particularly in the presence of low expiratory flow rates and short expiratory times, the CO2 concentration profile may be severely distorted. In worst case situations end tidal CO2 plateaux may not be recognized or alternately artifactual plateaux may be produced. Sample flow rate and sample cell volume are the most important parameters while distortion within the sample tube itself is relatively less important.

Carbon Dioxide↗
PubMed1985

A mathematical model for gas exchange in the fish gill based on non-linear blood gas equilibrium curves.

A mathematical model for gas exchange in fish gills is presented, which makes allowance for the non-linear nature of the oxygen and carbon dioxide equilibrium curves of blood, for the uneven distribution of diffusion conductance along the secondary lamellae, and for coupling of oxygen and carbon dioxide exchange through the Bohr and Haldane effects. The model demonstrates that for oxygen loading in the gill the sigmoid equilibrium curve is superior to a linear one, whereas the non-linearity of the carbon dioxide equilibrium curve does not significantly affect carbon dioxide exchange and that the Bohr and Haldane effects have importance only for carbon dioxide exchange. It is also shown that the arterial and expired gas tensions and concentrations are unaffected by whether the bulk of the diffusion conductance is at either the afferent or the efferent end of the individual lamellae, provided that the total conductance is unchanged.

Animals↗
PubMed1986

The rate of oxygen release and its effect on capillary O2 tension: a mathematical analysis.

The time required by the red blood cells (RBC) to release the O2 needed by the tissues may be rate-limiting under conditions of reduced O2 supply (DO2). A time-dependent mathematical model of capillary O2 transport is developed to explore the effect of RBC deoxygenation kinetics on the intracapillary plasma PO2. The tissue capillaries are represented by a series of perfectly mixed compartments. In each compartment O2 is removed by the tissues as a chemical reaction takes place between O2 and oxyhemoglobin (HbO2). A system of differential equations is formulated to monitor changes in the intracapillary concentration of HbO2 and plasma O2. These equations allow for changes in blood flow, arterial oxygenation, capillary transit time, rate of O2 uptake, hemoglobin concentration and the position of the oxyhemoglobin dissociation curve. The predicted capillary PO2 for conditions of normal O2 supply is less than the PO2 calculated assuming an instantaneous rate of RBC deoxygenation. This difference in plasma PO2 is not present in the venous end of the capillary, since at this point oxyhemoglobin and plasma O2 have sufficient time to re-establish equilibrium. The discrepancy in PO2 profiles is magnified by anemia, [( Hemoglobin] = 5 g/dl), and hypoxemia, (PaO2 = 25 Torr). For these conditions of severe DO2 reduction, the end-capillary PO2 is significantly less than the venous PO2. These results suggest that (1) the kinetics of RBC deoxygenation can play an important role in the delivery of O2 to the tissues, and (2) the venous PO2 is not always an accurate measure of the end capillary PO2.

Anemia↗
PubMed1994

A diameter-based reconstruction of the branching pattern of the human bronchial tree. Part II. Mathematical formulation.

In this paper we present the mathematical details of the diameter-based reconstruction technique used in the companion paper (Phillips et al., 1994 - referred to below as Part I) to analyse the morphometric data of Raabe et al. (1976) on the human bronchial tree. In the first section we outline the technique as applied to the incomplete set of measurements in order to estimate properties of the bronchial tree as a whole; in the second section we consider what form these properties would take if the bronchial tree were geometrically self-similar, as has often been assumed to be approximately the case.

Airway Resistance↗
PubMed1984

Mathematical model for cadmium kinetics in the isolated perfused rat liver system.

The isolated perfused rat liver (IPRL) preparation has previously been used to investigate cadmium kinetics. A mathematical model which has been developed to simulate cadmium kinetics in the IPRL is described. The model takes into consideration binding of cadmium to both intra- and extracellular proteins and the mechanisms of membrane transport. In addition, the competitive interaction of cadmium with endogenous zinc is incorporated into the model. Model simulations of the behavior of cadmium and zinc in the perfusion medium, liver, and bile are compared to results from IPRL experiments involving cadmium doses ranging from 0.29 to 15.6 mumol. A major contribution of this model is the identification, from a kinetic point of view, of two high-molecular-weight classes of intracellular cadmium-binding species which can be identified by two distinct peaks in Sephadex G-75 profiles of hepatic cytosol. This model can be utilized for the quantitation of kinetics based on specific mechanisms involved in cadmium hepatic kinetics.

Animals↗
PubMedDate not supplied

A mathematical analysis of the mortality kinetics of Drosophila melanogaster exposed to gamma radiation.

A mathematical model with nonlinear time-varying characteristics has been developed which describes the relationship between the kinetics of natural aging and radiation-induced delayed mortality. Based on this model, it appears that there is an immediate effect of radiation which is continuously, but nonlinearly, increasing in severity. Two phases appear in this variation, corresponding to the two phases (plateau and dying phase) of the mortality curves for control populations. Accordingly, S/E (survival time post-irradiation/further expectation of life) can best be interpreted as an increasing function during the plateau phase of normal mortality curves, which levels off during the ensuing dying phase.

Aging↗
PubMed1981

Modeling cellular systems and aging processes: I. Mathematics of cell system models-a review.

A review of the literature on mathematical models of populations of cellular systems is presented. Continuous, discrete, and stochastic models are presented in a semihistorical manner as a prelude to answering the question of how to model an asynchronously dividing cellular system. This analysis is then broadened, in an attempt to broach the more general question of modeling the distribution of a set or collection of cell properties through an asynchronously dividing cellular system. Such properties might be cell motility, cell cycle length, time to mitosis, or number of epigenetic particles. It is shown that one fruitful approach to this modeling question is a coupled continuous-probabilistic model. The ramifications of this type of formalism are discussed.

Aging↗
PubMed1992

Mathematical modeling of radionuclide dispersion in the Pripyat-Dnieper aquatic system after the Chernobyl accident.

The Chernobyl accident heavily contaminated the largest aquatic system in the Ukraine, requiring the development of a model-based decision support system in the field of aquatic radioecology. The main objectives of the system were to simulate and predict radionuclide dispersion in the Pripyat-Dnieper River-reservoir system, assess the effectiveness of special hydraulic countermeasures designed to decrease the rate of radionuclide dispersion in the water bodies, and support the Dnieper reservoirs' management operations. A hierarchy of mathematical models was developed. A two-dimensional (2-D) vertical-longitudinal model, a 2-D lateral-longitudinal model, a one-dimensional (1-D) channel model and a box-type model are briefly presented. These models describe the main features of radionuclide dispersion, including the processes governing radionuclide-sediment interactions. Examples of the models' applications are presented to show the peculiarities of radionuclide dispersion in this aquatic system.

Accidents↗
PubMed1984

Kinetic study on the initial stage of the fibrinogen-fibrin conversion by thrombin. (1) Application of mathematical treatment to turbidimetrical method.

Kinetics on the initial reaction of the fibrinogen-fibrin conversion catalyzed by thrombin was studied by turbidimetrical measurement. The turbidity change caused by the conversion reaction was analyzed by a mathematical treatment, assuming that the dimer formation of fibrin monomers was the rate-determining reaction in the stage of polymerization. The obtained relations were investigated under experimental conditions at neutral pH and at low ionic strength, in which fast polymerization rate of fibrin monomers can be expected in comparison with the rate of enzyme reaction. The experimental results analyzed from turbidity-time curves were generally in agreement with theoretical prediction. On the other hand, the plots relating to the enzyme concentration did not lead to anticipated linear relationship. Hence, it was concluded that every fibrin monomer did not always polymerize via dimer formation, but that dimers of fibrin monomers behaved as nuclei for polymerization.

Animals↗
PubMed1991

A mathematical model of the kinetics of platelets and plasma hemostasis system interaction.

A mathematical model of the kinetics of platelet-activated blood coagulation is presented. Non-linear positive feedbacks due to the action of co-factor Va and VIIIa, thrombin-induced platelet activation, the secretion of factor V by platelets are taken into account. The intrinsic pathway is shown not to be activated in the absence of platelets for small stimulation intensities. The activation occurs if initial platelet activation by inductors other than thrombin exceeds a threshold value.

Blood Coagulation↗
PubMed1995

Oscillating prostacyclin and thromboxane generation by human vessels: biological and mathematical evidence for negative feedback control.

The presented study investigates the time-dependent release of PGI2 and TXA2 by isolated human umbilical veins in vitro using the radioimmunoassay for measurement. After changing the nutritional fluid--Krebs-Henseleit solution at pH 7.4, 37 degrees C, 95% O2/5% CO2--the release graph oscillates. These oscillations with time were verified by variance analysis and are very similar for both substances. This indicates one or several negative feedback mechanisms acting on the common path of synthesis from the membrane-bound phospholipids to PGH2, which are effective in the regulation of eicosanoid biosynthesis in vitro. A mathematical function describing the observed PGI2 and TXA2 synthesis is communicated.

Embryo, Mammalian↗
PubMed1994

Life-span of irradiated mammals. Mathematical modelling.

A mathematical model of the mortality dynamics of irradiated mammals is developed. It relates the statistical biometrical functions with the statistical and kinetical characteristics of the critical systems in the organism. This model can be used for predicting the life shortening of irradiated mammals.

Animals↗
PubMed1981

Pulsatile pressure and flow in arterial stenoses simulated in a mathematical model.

This paper presents the detailed pulsatile pressure and flow velocity patterns inside an axis symmetric stenosis model with 75% constriction. The pressure and velocities have been calculated by solving the Navier-Stokes equations by the finite element method, the velocity profile in a straight tube caused by a pulsating driving pressure has been calculated first and then used as a boundary condition for the stenosis calculations. The results of the mathematical simulations of the stenosis model have been obtained in terms of velocity vectors, streamlines and isobars at 16 different instances in time, each 15 degrees apart during a cardiac cycle. The calculated velocity field shows that a vortex is developed at the wall distal to the stenosis as the velocity decreases from the peak systolic value. At the site of the vortex, a local pressure minimum is found due to the conversion of pressure to kinetic energy. when the flow is reversed, the reversal occurs first along the wall, thus forcing the vortex toward the centre of the tube. As the reverse flow velocity increases, a vortex is also developed at the proximal site of the stenosis.

Arterial Occlusive Diseases↗
PubMed1989

A mathematical analysis for the modelling of trabecular bone.

We present a mathematical analysis of trabecular bone which may be applied to develop dynamic computer simulations of the musculoskeletal system. We have derived an algorithm which can be used to study the genetic limitations within which skeletal articulations may function successfully. We believe that our model will help other workers to advance the understanding of the interplay between genetic and environmental influences in the growth, modelling and degeneration of osseous tissues.

Animals↗
PubMed1990

Patient realignment in magnetic resonance imaging of the head: an algorithm using mathematical morphology for feature extraction.

To develop a technique for automatic patient realignment in magnetic resonance imaging (MRI), it is essential to extract key features automatically from the various slices of the head as accurately as possible. Such features include the brain, the brain stem, the pons, the corpus callosum and the cerebellum. A feature extraction algorithm has been developed which is based on thresholding a region to a common grey level and then applying mathematical morphology to produce a binary regular region. In addition, a region-filling algorithm has been developed to obtain the complete feature. The scans derived from the T1 spin-lattice relaxation time, which are the fastest of the MRI scans, are used in patient realignment to provide highly textured images. These are difficult to segment using conventional thresholding or edge enhancement techniques due to their 'grainy' appearance, which makes it difficult to isolate key features from the other components found in the slice. We have developed a method for the accurate extraction of the corpus callosum, the cerebellum and the brain area in a sagittal scan of the head. This is carried out by selective thresholding designed to remove the low texture content and then applying morphological techniques.

Algorithms↗
PubMed1992

Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation.

An exact knowledge of the human fetus's respiratory mechanisms is still lacking; in particular, the role of human placental anatomy in oxygen exchange has not yet been studied satisfactorily. In this paper, a mathematical model of placenta as O2 exchanger between maternal and fetal blood was developed; it led to the solution of equations based upon diffusion laws and the haemoglobin dissociation curve. Particular care was taken to represent the regimen of laminar motion or whirling into the capillaries. Theoretical results were compared, under physiological conditions, with clinical data relating to fetal oxygenated blood p O2 during the second half of gestation (20th-38th weeks), and a theoretical confirmation of the decreasing effectiveness of placental O2 exchange during gestation was found. The result was able to describe oxygen exchange during a period in which clinical data are scanty (23rd-30th weeks). The effects of some pathological events on O2 exchange were then simulated. Model parameters were changed to simulate the effects on oxygen exchange of some typical pathological variations of placental anatomical features: exchange surface thickness and capillary length. The curves obtained for different gestational ages can easily be correlated with echographic measures of placental volume and dimensions of placental capillaries. The results also show that the human placenta is more sensitive to pathologies when it is young than at term of gestation.

Capillaries↗
PubMed1995

A mathematical model of agonist-induced propagation of calcium waves in astrocytes.

In astrocytes, calcium signals evoked by neurotransmitters appear as waves within single cells, which spread to other cells in the network. Recent analysis has shown that waves are initiated at a single invariant site in the cell and propagated within the cell in a nonlinear and saltatory manner by regenerative amplification at specific predestined cellular sites. In order to gain insight into local cellular waves and wave collisions we have developed a mathematical model of cellular wave amplification loci. This model is in good agreement with experimental data which includes: ambient calcium gradients in resting cells, wave origination and local amplification and generation of local waves. As observed in experiments, the model also predicts that different locations in the cell can have different frequencies of oscillation. The amplification loci are thought to be specialized areas of the endoplasmic reticulum membrane containing a higher density or higher sensitivity of IP3 receptors. Our analysis suggests that the cellular loci act as weakly coupled oscillators each with its intrinsic latency and frequency of oscillation. Thus the appearance of the propagated calcium wave may be a reflection of these differences rather than an actual diffusional wave propagation.

Animals↗
PubMed1990

A mathematical model for cadmium in the stone loach (Noemacheilus barbatulus L.) from the River Ecclesbourne, Derbyshire.

A mathematical model which linked metabolism of stone loach with cadmium dynamics was developed using information from laboratory experiments and field studies. Three possible sources of cadmium were distinguished: water, food, and sediment. Predicted results over 1 year were compared with field observations from three sites in Derbyshire. The model adequately predicted growth of fish for all three sites. Predicted cadmium levels in loach were in good agreement with measured levels in fish from all three sites despite the fact that concentrations of cadmium in the environment were kept constant during each simulation. The weight of fish affected the relative importance of different pathways of cadmium intake under similar conditions. Uptake from water contributed substantially to body burden even though the concentration in water was lower than that in food or in sediment. However, uptake from both food and sediment could not be ignored given the measured levels of cadmium in the field. The relative importance of uptake from the three sources also differed with site. The model showed that metabolism, affected by temperature, is important to the dynamics of cadmium in the stone loach.

Animals↗