Regulation of the blood circulation system in hypertensive crises using mathematical analysis of the cardiac rhythm

Regulation of the circulatory system in hypertensive crises was studied using mathematical analysis of the cardiac rhythm. The study involved 166 patients from age 29 to 73 years with hypertension stage II–III. The cardiac rhythm variability was assessed for 10-min intervals by parameters of the regulatory system activity (according to R.M. Baevskiiet al.). In hypertensive crisis, the cardiac rhythm variability was decreased, and the activity of systems regulating blood circulation was increased, compared to both the normal and the crisis-free period. Therefore, the determination of parameters of cardiac rhythm variability has an additional diagnostic value. Changes in these parameters in hypertensive crisis depend on the duration of hypertension, the patients’ age, and dysfunction of target organs. Changes in the cardiac rhythm variability persisted after normalization of arterial pressure in the postcrisis period, and this indicates that the patients’ condition was not stabilized during hospital treatment and prolonged supervised hypotensive therapy was required.     

Fitting the Incidence Data from the City of Campinas,Brazil, Based on Dengue Transmission Modellings Considering Time-Dependent Entomological Parameters

Four time-dependent dengue transmission models are considered in order to fit the incidence data from the City of Campinas, Brazil, recorded from October 1^st 1995 to September 30^th 2012. The entomological parameters are allowed to depend on temperature and precipitation, while the carrying capacity and the hatching of eggs depend only on precipitation. The whole period of incidence of dengue is split into four periods, due to the fact that the model is formulated considering the circulation of only one serotype. Dengue transmission parameters from human to mosquito and mosquito to human are fitted for each one of the periods. The time varying partial and overall effective reproduction numbers are obtained to explain the incidence of dengue provided by the models.     

Two-phase model of the kinetics of growth of Rhizopus oligosporus in membrane culture

An empirical model was developed to describe a growth profile occurring in solid-state fermentation (SSF), namely that consisting of an initial period of rapid acceleration followed by an extended period of deceleration. This kinetic profile is not adequately described by the logistic model. The empirical model is based on the concept of active and nonactive hyphal segments. Exponential and deceleration growth phases are modeled. The model parameters can be determined directly from the dry-weight profile and they depend on the growth medium present. The model suggests that, at the instant the culture enters the deceleration phase, there is a 71% to 86% decrease in the number of actively extending hyphal tips and that, during the deceleration phase, there is an exponential decay in the number of active hyphal segments, with a first-order decay constant of 0.042 to 0.072 h(-1).     

On linear perturbations of the Ricker model

A class of linearly perturbed discrete-time single species scramble competition models, like the Ricker map, is considered. Perturbations can be of both recruitment and harvesting types. Stability (bistability) is considered for models, where parameters of the map do not depend on time. For models with recruitment, the result is in accordance with Levin and May conjecture [S.A. Levin, R.M. May, A note on difference delay equations, Theor. Pop. Biol. 9 (1976) 178]: the local stability of the positive equilibrium implies its global stability. For intrinsic growth rate r-->infinity the way to chaos is broken down to get extinction of population for the depletion case and to establish a stable two-cycle period for models with immigration. The latter behaviour is also studied for models with random discrete constant perturbations of recruitment type. Extinction, persistence and existence of periodic solutions are studied for the perturbed Ricker model with time-dependent parameters.     

Chronometric study of a posturo-kinetic program associated with voluntary movement

Posturo-kinetic programming was investigated by a simple reaction time paradigm. Standing subjects performed voluntary upper limb elevations differing by the importance of their destabilizing effect on the initial balance. It was shown that: The reaction time varied according to the destabilizing effect of the forthcoming movement. These variations were due to differences in the duration of postural adjustments which were shown to precede voluntary movement. Duration of pre-motor period, corresponding to delay between the response signal and the onset of the earliest postural adjustment, did not depend on parameters of the forthcoming movement.     

Analysis of life tables with grouping and withdrawals.

A number of individuals is observed at the beginning of a period. At the end of the period the number is surviving, the number who have died and the number who have withdrawn are noted. From these three numbers it is required to estimate the death rate for the period. All relevant quantities are supposed independent and identically distributed for the individuals. The likelihood is calculated and found to depend on two parameters, other than the death rate, and to be unidenttifiable so that no consistent estimators exist. For large numbers, the posterior distribution of the death rate is approximated by a normal distribution whose mean is the root of a quadratic equation and whose variance is the sum of two terms; the first is proportional to the reciprocal of the number of individuals, as usually happens with a consistent estimator; the second does not tend to zero and depends on initial opinions about one of the nuisance parameters. The paper is a simple exercise in the routine use of coherent, Bayesian methodology. Numerical calucations illustrate the results.     

Etiology of the supernormal period.

In many excitable cells, there is a time after the action potential when the threshold for eliciting a second action potential is lower than it is in the steady state. The Hodgkin and Huxley (1952) equations predict such a supernormal period. Using their model, it is shown that the supernormal period results from the slow kinetics of the potassium current and does not depend on sodium current activation or inactivation or on the after-depolarization.     

Lipid peroxidation and myocardial contractile function in the post-ischemic period depending on the level of hypothermic protection of the heart]

The experiments on rats isolated hearts showed lipid peroxidation state to depend on myocardial cooling level in ischemic period. Cooling to 8-12 degrees C does not induce significant impairment in the system of lipid peroxidation/antioxidant activity, thus preventing the development of reperfusion impairment in cardiac activity restoration. Temperature decrease to 4-6 degrees C during the ischemic period results in lipid peroxidation, antioxidant cell system exhaustion and impairment of contractive myocardial function in reperfusion.     

The algal flora in the Thermal Baths of Montegrotto Terme (Padua). Its distribution over one-year period

The results of a one year period study on the algal flora in the muds and in the spring water of Montegrotto Terme (Padua) are reported. Temperature and pH do not seem to have any direct influence on phytoplankton population, but their variation must depend from other not yet identified factors.     

Delayed responses of ganglion cells in the frog retina: the influence of stimulus parameters upon the discharge pattern

The delayed response from frog retinal ganglion cells is preceded by a long silent period which has been shown to depend upon (i) intensity of the stimulus light flash, (ii) background illumination, and (iii) instantaneous level of adaptation. Also the duration of the delayed response and the total number of spikes elicited are functions of these three parameters. A linear relationship has been found between the silent period and both delayed response duration and total number of spikes. Double-flash experiments indicate that the ganglion cell output is strongly inhibited during the silent period. Experiments using an inhomogenous stimulus field have led to the conclusion that parts of the receptive field contribute independently to the delayed response.Supported by the Deutsche Forschungsgemeinschaft.S. G. P. was a postdoctoral fellow supported by a U. S. Public Health Service grant, NIH 1 F 2 NB 24,455-01.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

Parameters of hemolysis by sodium dodecyl sulfate as an indicator of the structural states of erythrocyte membranes]

The relationship between the parameters (percentage and rate) of hemolysis by sodium dodecyl sulfate and the time of incubation of human erythrocyte suspensions in glucose-free medium at 37 degrees C was studied. The polyphasic changes in the parameters were found, which depend on the mode of pretreatment: ATP depletion by iodoacetate, heat denaturation of spectrin, and treatment of cells by valinomycin. It was found that the percentage and rate of detergent hemolysis do not always change in parallel.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

Morphofunctional changes in the long tubular bones of animals which have developed while readapting after physical loads

The investigation has been performed on 120 white male rats of Wistar line. By means of the morphometry, electron microscopy and chemical methods dynamics of readaptive changes have been studied in long tubular bones during the period, when the effect of physical loadings both of dynamic and static character and of various intensity has been stopped, up to the old periods of the animals' life. Readaptation after moderate dynamic and static loadings is occurring for a long time and steadily. The changes caused by static loadings are nearly completely restored in a year. Morphofunctional rearrangements of the long tubular bones in the readaptation process after moderate dynamic loadings is characterized by residual manifestations. Prolonged readaptation after intensive physical loadings does not result in a complete restoration of all the parameters studied concerning growth and skeletal development. An intensive dynamic loading produces more stable changes, that are not subjected to a complete correction even after a passive readaptation for a year. Readaptation morphofunctional rearrangements of the long tubular skeletal bones depend on conditions of the previous regimen of the motor activity.     

Fluorescence decay studies of reduced nicotinamide adenine dinucleotide in solution and bound to liver alcohol dehydrogenase.

The monophoton counting technique was used to obtain the fluorescence decay kinetics of NADH (dihydronicotinamide adenine dinucleotide) bound to LADH (HORSE LIVER ALCOHOL DEHYDROGENAS). It was found that the fluorescence decay of the enzyme complex did not follow a single exponential decay law but that the data could be well described as a sum of two exponentials. The decay parameters of the enzyme complex do not depend on the degree of binding-site saturation. These results are interpreted in terms of a reversible excited-state reaction forming a nonfluorescent product. Fluorescence decay kinetics are also reported for NADH and related molecules in solution. The decay parameters, fluorescence emission maxima, and fluorescence intensities depend on solvent polarity and viscosity.     

The effect of cholesterol on the function of staphylotoxin channels

Bilayer lipid membrane (BLM) formed from lecithin and lecithin-cholesterol mixtures by Mueller and Montal were used. It was found that the parameters of ST-channel functioning did not depend on the presence of the carbohydrate solvent. The 0.5 molar cholesterol in BLM markedly influenced the characteristic relaxation time depending on the electric field vector direction through the membrane, and increasing them only when the potential from the side of added channel-former was negative.     

Contribution of leaf nitrogen to photosynthetic gas exchange in contrasting rice (Oryza sativa L.) cultivars during the grain-filling period

Photosynthetic parameters and leaf carbon isotope composition (??¹³C) in contrasting rice genotypes in relation to supplemental nitrogen (N) application and water management during the grain-filling period were compared. The changes in stomatal conductance (g _s) and ratio of intercellular to ambient CO₂ mole fraction (C _i/C _a) depended on the leaf nitrogen concentration (leaf N) in both ??Hinohikari?? (temperate japonica genotype) and ??IR36?? (indica genotype). In ??Hinohikari??, ??¹³C reflects photosynthetic gas exchange during the grain-filling period, which is indicated by the significant response of ??¹³C to leaf N. In contrast, in ??IR36?? ??¹³C did not depend on leaf N. This varietal difference in ??¹³C to leaf N can be attributed to a difference in the timing of leaf senescence. In ??IR36??, leaf N and photosynthetic parameters decreased more rapidly, indicating earlier senescence and a shorter grain-filling period in comparison with ??Hinohikari??. The significant increase in shoot dry mass in ??Hinohikari?? resulting from supplemental N application, compared with nonsignificant effect observed in ??IR36??, suggests that the timing of senescence in relation to the grainfilling period has a preponderant influence on productivity.     

Combined effect of gamma-irradiation and sodium nitrite on the oxidative sensitivity of rat hemoglobin

gamma-Irradiation has been defined to increase in the rats blood the methemoglobin level providing for shortening the initiation phase and accelerates the autocatalytic phase initiation, reduces the period of half transforming hemoglobin into methemoglobin and increases the velocity of its oxidation. Alongside with the latter there is observed a violation of methemoglobin concentration growth dependence on the animals irradiation dose (in the range of 0.16-0.50 Gr). The hemoglobin oxygenation reaction kinetics with the initial level of hemoglobin unexceeding 3% has been determined as having a biexponential character. The reaction kinetics parameters don't depend on ionizing radiation and number of sodium nitrite oxidized subunits formed in the process of reaction in the case if their composition unexceeds 50% of the total level.     

Autowave processes in a distributed chemical system

The autowave processes with a characteristic wavelength and oscillation period may arise under some initial conditions in a uniform active medium. The wavelength and period depend on the chemical and physical parameters of the system and are independent of the initial and boundary conditions and of the system linear size. The processes occur in a homogeneous solution in the course of an oscillating chemical reaction. Similar processes may play an important role in the phenomena of short-term memory, cardiac arrhythmia, morphogenesis and prebiological evolution.Different types of structures are discussed, and experimental data and mathematical models are presented.