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PubMed1984

[A semiempirical mathematical model for assessment of PH3 residues as exemplified by phosphine-fumigated hazelnuts].

A mathematical model for the calculation of residues of PH3 in fumigated hazelnuts in dependence on dosage, fumigation- and storage time is discussed. The model is based on the physical process of the diffusion of a gas out of a sphere. An empirical dependence of the diffusion coefficient on the residue levels can be observed. Adequate agreement is obtained between calculated and experimental values.

Food Contamination↗

PubMed1987

Antigenic relationships between avian paramyxoviruses. II. A combinatorial mathematical model of antigenic kinship.

A combinatorial mathematical model describing the antigenic relationships found between different avian paramyxovirus (PMV) serotypes (Lipkind and Shihmanter, 1986) is presented. According to the model, the network of the antigenic interconnections is determined by the specific combinatorial sets of antigenic determinants, some of them being serotype-specific and the others being common to certain other avian PMV serotypes. The suggested model is based on certain postulates concerning PMV virion structure; the bifunctional organization of PMV haemagglutinin-neuraminidase (HN) glycoprotein, its amount per virion and a mechanism of antibody-caused inhibition of its functional activities; the definition of an antigenic determinant as an elementary unit inducing and reacting only with a homologous type of antibodies. The model interprets in specific terms some serological results, in particular the old but mysterious phenomenon of asymmetric cross reactivity.

Animals↗

PubMed1994

Mathematical modelling for the generation of L-[3-2H,3-13C]lactic acid isotopomers by erythrocytes exposed to either D-[1-13C]glucose or D-[6-13C]glucose in the presence of 2H2O.

The production of C3-trisdeuterated, bisdeuterated, monodeuterated or non-deuterated L-[3-13C]lactate by human erythrocytes exposed to either D-[1-13C]glucose or D-[6-13C]glucose in the presence of 2H2O can be assessed by 13C NMR spectroscopy. Such a deuteration may occur at the level of the reactions catalyzed by phosphoglucoisomerase, phosphomannoisomerase, pyruvate kinase and glutamate-pyruvate transaminase. In this report, a mathematical model is proposed for the analysis of experimental data. It allows to estimate the relative extent of deuteration at each step of D-glucose metabolism. This approach may thus provide novel information on the extent of back-and-forth interconversion of either hexose 6-phosphates in both the phosphoglucoisomerase and phosphomannoisomerase reactions or pyruvate and L-alanine in the reaction catalyzed by glutamate-pyruvate transaminase.

Alanine Transaminase↗

PubMed1982

Analysis of the ICP pulse-pressure relationship as a function of arterial blood pressure. Clinical validation of a mathematical model.

The influence of arterial blood pressure (ABP) on the intracranial pulse pressure relationship (PPR) was studied in 17 patients in 29 recordings, with a total period of registration of 71.5 hours. The relationship between ICP and ABP was analysed by sampling the data every 15 seconds during spontaneous fluctuations of both these variables, and the analysis was performed on the basis of a mathematical model which includes pulsatory components. MABP and ABP amplitude had an opposite effect on the slope of PPR. Flattening of the PPR slope was caused by a MABP increase or an ABP amplitude decrease. The slope became steeper with decreasing MABP or increasing ABP amplitude. In accordance with the theoretical assumptions the quotient MABP/ABP-AMP was found to be suitable to express these opposite effects on PPR. Qualitatively, the same pattern of reaction was found in all patients. Rapid changes in PPR occurring during monitoring can be explained by a change in MABP/ABP-AMP relationship, regardless whether ABP changes influence intracranial elastance or not. The breakpoint of the PPR was recorded only on two occasions and could be explained in one by the influence of ABP. Monitoring of PPR as a measure of intracranial elastance and correlation of PPR with the patient's condition it not permitted unless at least the influence of ABP is analysed in each individual case.

Adult↗

PubMed1993

A mathematically designed STS primer without any mismatches for direct sequencing of cosmid DNA clones.

We report here a new method for the direct sequencing of large DNA inserts of cosmid clones from human chromosomes using STS primers of 14 nucleotides without any mismatches, which are designed from results of a mathematical analysis. It is clear that STS primer of 14 nucleotides is optimum for direct sequencing of cosmid recombinant DNA clones. We also provide examples of direct sequencing of cosmid clones of human chromosome 21 using these STS primers.

Animals↗

PubMed1984

Direct observation of enzyme substrate complexes by stopped-flow fluorescence: mathematical analyses.

The fluorescence changes which occur upon the interaction of enzyme and substrate under stopped-flow conditions can provide a sensitive means to directly observe ES complexes. The interconversion of the intermediates during catalysis causes changes in fluorescence, signaling directly their existence, and allowing their quantitation. We have studied extensively an approach which measures radiationless energy transfer (RET) between enzyme tryptophanyl residues and a fluorescent peptide or ester substrate. Our studies of a number of proteolytic enzymes have validated the approach, which is sensitive and applicable to a variety of enzymes under a wide range of experimental conditions, including subzero temperatures. Direct excitation of fluorescent substrates can also be used to observe ES complex formation and breakdown and is complementary to the RET approach. Here we review both the RET and direct excitation kinetic approaches, with particular emphasis on the mathematical foundations we have developed which are critical to the successful interpretation of these or any other spectroscopic approach which yields a signal that is unique to the ES complex.

Carboxypeptidases↗

PubMed1975

Mathematical modeling of differentiation in Dictyostelium discoideum.

Methods for the dynamic analysis of biochemical differentiation are presented. These are demonstrated in the analysis of biochemical differentiation of the carbohydrate system in D. discoideum. Procedures for simplification which are presented are projection and contraction of the system trajectory in state space and the generation of reduced equivalent dynamic metabolic networks. The importance of the hierarchical structure of differentiating systems is discussed and the concept of a dynamic embedding diagram is introduced. It is shown that complex systems must be analyzed on an epoch by epoch basis, each epoch being a period of time characterized by a constant dynamic embedding diagram, and that widely different time scales and state space scales may be necessary in different epochs. In particular there is no a priori lower limit to the time scale which may be necessary during the analysis. Some problems in mathematically defining differentiation are discussed.

Carbohydrate Metabolism↗

PubMed1987

A mathematical approach to cognitive processes.

A mathematical formalization of cognitive processes based on concepts previously given in Experientia is presented. Cognitive processes are described as a set of exponentially decaying interaction probabilities determined by previous interactions between different elements and an association parameter, the inverse of the cognitive stability. The interactions occur in a 'cognitive string' surrounded by a 'cognitive plasma' which carries the contextual information. The 'complexity' of a cognitive process is proportional to time.

Cognition↗

PubMed1989

[Evaluation of the applicability of a mathematical model in the x-ray cephalometric diagnosis of sagittal bite anomalies. A clinical test].

The mathematical model (Järvinen) for measuring the sagittal difference between the maxillary and mandibular apical bases has been clinically tested. The material for this study consisted of 30 lateral skull radiographs of orthodontically untreated children (aged seven to 15 years) with different types of skeletal and/or dento-alveolar malocclusions. A comparison of the model with two conventional and two more developed methods to measure the sagittal apical base difference showed that the correlation between the new and the older methods increased as the errors of the older methods were eliminated. The results seemed to indicate that sagittal malocclusions could be accurately diagnosed by means of the model.

Adolescent↗

PubMed2000

Arterial baroreflex influence on heart rate variability: a mathematical model-based analysis.

The influence of the arterial baroreflex on the heart rate variability is analysed by using a mathematical model of heart rate baroreceptor control. The basic mechanisms of the model, sufficient to elicit heart rate variability include: systemic circulation, a non-pulsatile cardiac pump and nonlinear negative feedback simulating arterial baroreflex closed-loop control of the heart rate (-3 bpm/mmHg as maximum reflex sensitivity). The latter reproduces, through two distinct delayed branches (0.8 and 2.8 s), the short-term autonomic control effected respectively by sympathetic and parasympathetic divisions on the sinus node. By means of this model, two distinct self-sustained oscillatory components with incommensurate frequencies (0.1 and 0.26 Hz) are reproduced. Frequencies of these two oscillatory components closely agree with the main heart rate rhythms in humans (0.09 +/- 0.01 Hz and 0.26 +/- 0.01 Hz). When sympathetic-mediated regulation prevails over parasympathetic activity, simulated heart rate oscillation is characterised by a low frequency (approximately 0.1 Hz). On the other hand, a high-frequency oscillatory component (approximately 0.26 Hz) appears when enhanced vagal activation or partial inhibition of the sympathetic control is simulated. When both autonomic divisions are operative, both low- and high-frequency components are present and the heart rate oscillates quasi-periodically. This variability in heart rate at different frequencies is reproduced without including outside perturbations and is due to the nonlinear delayed structure of the closed-loop control. Bifurcation theory of nonlinear system is used to explain the high sensitivity of the heart rate oscillatory pattern to model parameter changes.

Baroreflex↗

PubMed1987

Mathematical and mechanical modeling of heat transport through the heart.

Pulmonary artery blood temperature manifests large variations which obscure the measurement of cardiac parameters by thermodilution techniques. We have created three mathematical models of heat flow through the heart in order to better understand the origins of the temperature fluctuations in the pulmonary artery. These lumped parameter models are based on a serial connection of two mixing chambers, which correspond to the atrium and ventricle of the heart. We have used the models to predict temperature fluctuations in the outlet, based on measurements of inlet flow, inlet temperature, and the timing of the cardiac cycle, of a mechanical right artificial heart in a mock circulatory loop. The most complex model accurately predicts the outflow temperature from the input variables and provides a quantitative description of heat transport across the heart under many operating conditions. The simplified models illustrate the conditions under which is possible to predict the outflow temperature from the inflow temperatures alone.

Animals↗

PubMed1988

Mathematical evidence for flow-induced changes in myocardial oxygen consumption.

The objective of this investigation was to aid in the determination of the mechanism by which oxygen consumption changes in proportion to coronary perfusion pressure or coronary blood flow. A mathematical model of oxygen transport and consumption in the isolated-perfused heart was developed, based on data from an autoregulating, cell-free perfused, externally paced, isovolumic feline heart preparation. The model features the unique combination of Michaelis-Menten kinetics, and one-dimensional (axial) diffusion in radially well-mixed tissue. An adaptive finite-difference integration routine was used to solve the resulting third order stiff two-point boundary value problem. A simplex minimization was employed to determine the parameter values that minimized the squared difference between the model and the experimental data in terms of tissue PO2 distribution (histograms). Different cases of the model representing pressure-induced, flow-induced, and "magnified" flow effects were run. The flow-dependent oxygen consumption version of the model produced a histogram squared error 30% lower than the pressure-induced version and 5% lower than any other case. The model and a critical review of the literature indicate that a flow-related mechanism is responsible for this phenomenon. Evidence also demonstrates that the Michaelis-Menten kinetics constant is not constant for different oxygen tensions.

Coronary Circulation↗

PubMed1988

A mathematical study of human intracranial hydrodynamics. Part 1--The cerebrospinal fluid pulse pressure.

An original mathematical model of human intracranial hydrodynamics is proposed. Equations able to mimic the behavior of the intracranial arterial vascular bed, intracranial venous vascular bed, cerebrospinal fluid absorption and production processes, and the constancy of overall intracranial volume are separately presented and discussed. The model parameters were given normal values computed using physiological considerations and recent anatomical data. In this paper the model is used to simulate the genesis and morphology of the intracranial pressure pulse wave. In particular, dependence of the intracranial pressure pulse amplitude on mean intracranial pressure, obtained from the model, shows excellent agreement with recent experimental findings. The model explains the intracranial pressure pulse wave as the result of the pulsating changes in cerebral blood volume (related to cerebrovascular compliance) which occur within a rigid space (i.e., the craniospinal compartment). At low and medium values of intracranial pressure, the intracranial pressure pulse amplitude mainly reflects the cerebral pressure-volume relationship. However, during severe intracranial hypertension, an abrupt increase in the cerebrovascular compliance becomes evident, which is reflected in an abrupt increase in the intracranial pressure pulse wave.

Cerebrospinal Fluid↗

PubMed1988

A mathematical study of human intracranial hydrodynamics. Part 2--Simulation of clinical tests.

The mathematical model of human intracranial hydrodynamics proposed in a previous paper is here used to simulate the results of some dynamical tests of great clinical and physiological value and to analyze the blood flow pattern in the intracranial human basal arteries (especially in the internal carotid artery). Peak to peak amplitude of the blood flow waveform in the intracranial basal arteries, computed through the model, shows a significant increase at intracranial pressure levels above 50-60 mmHg, in accordance with recent experimental data. Moreover, diastolic blood flow appears to be largely sensitive to intracranial pressure changes during severe intracranial hypertension, whereas systolic blood flow is only slightly affected in this condition. The response of intracranial pressure to typical saline injection (volume-pressure response, steady state infusion and bolus injection tests) and to an abrupt obstruction in the extracranial venous drainage pathway is also well reproduced by the model. Finally, alterations in these responses, due to changes in some significant intracranial hydrodynamical parameters (i.e., the intracranial elastance coefficient and CSF outflow resistance) are presented.

Carotid Artery, Internal↗

PubMed1990

Mathematical models of the spatial distribution of retinal oxygen tension and consumption, including changes upon illumination.

To better understand oxygen utilization by the retina, a mathematical model of oxygen diffusion and consumption in the cat outer, avascular retina was developed by analyzing previously recorded profiles of oxygen tension (PO2) as a function of retinal depth. Simple diffusion modelling of the oxygen distribution through the outer retina is possible because the PO2 depends only on diffusion from the choroidal and retinal circulations and on consumption within the tissue. Several different models were evaluated in order to determine the best one from the standpoints of their ability to represent the data and to agree with physiological reality. For the steady state one-dimensional diffusion model adopted (the special three-layer diffusion model), oxygen consumption was constant through the middle layer and zero in the layers near the choroid and near the inner retina. On the average, the oxygen consuming layer, as found by nonlinear regression for each profile, extended from about 75% to 85% of the retinal depth from the vitreous. This is a narrow band through the mid-region of the photoreceptors. Oxygen consumption of the entire avascular retina, determined from fitting eight PO2 profiles measured in light-adapted retinas, averaged 2.7 ml O2(STP)/(100 g tissue.min), while the value determined from fitting thirty-two PO2 profiles measured in dark-adapted retinas averaged 4.4 ml O2(STP)/(100 g tissue.min). Consumption in the light was thus only 60% of that in the dark. This suggests that the outer retina is at greater risk of hypoxic injury in the dark than in the light, a finding of considerable clinical significance.

Animals↗

PubMed1992

Mathematical modelling of flow distribution in the human cardiovascular system.

The paper presents a detailed model of the entire human cardiovascular system which aims to study the changes in flow distribution caused by external stimuli, changes in internal parameters, or other factors. The arterial-venous network is represented by 325 interconnected elastic segments. The mathematical description of each segment is based on equations of hydrodynamics and those of stress/strain relationships in elastic materials. Appropriate input functions provide for the pumping of blood by the heart through the system. The analysis employs the finite-element technique which can accommodate any prescribed boundary conditions. Values of model parameters are from available data on physical and rheological properties of blood and blood vessels. As a representative example, simulation results on changes in flow distribution with changes in the elastic properties of blood vessels are discussed. They indicate that the errors in the calculated overall flow rates are not significant even in the extreme case of arteries and veins behaving as rigid tubes.

Blood Flow Velocity↗

PubMed1992

Mathematical model for the exchange of gases in the lungs with special reference to carbon monoxide.

A mathematical model has been formulated for the simultaneous exchange of gases O2, CO2, CO and N2 in the lungs. The model takes into account the physiological parameters, such as ventilation rate, diffusing capacity of the lungs, cardiac output, total volume of blood in the body and the interaction of gases in the blood. The nonlinear functions for representing O2, CO2 and CO dissociation curves have been used. The results predicted from the model are in good agreement with those based on the ventilation/perfusion relationships. The COHb build-up in the blood, computed from the model as a function of exposure time, is in good agreement with the experimental values. The consideration of capillary blood pO2 as a constant value, instead of an independent variable, is shown to introduce a maximum error of 0.25 per cent in the blood COHb. The model is applied to analyse the COHb levels at high altitude.

Carbon Monoxide↗

PubMed1995

The mathematics of radiation target analyses.

Radiation target theory has been extended to complex biochemical systems. Mathematical analyses are presented for multiple forms of biological active proteins, for the presence of large inhibitors or activators, for compounds which regulate rate or affinity and for multiple-step reactions. Several predictions of these models have been verified experimentally.

Animals↗