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At least 73 records · Page 4Linked to original sources

PubMed1988

The rate of gas-bubble growth in tissue under decompression. Mathematical modelling.

A mathematical model simulating the formation of gas bubbles in biological tissues under decompression is presented. It is written as a system of partial differential equations solved on a computer. For the nitrogen-oxygen gas mixture, used for respiration in deep-water immersions, the effects of the physico-chemical properties of the gases, the magnitude of pressure differentials and the density of bubble-formation centres on the bubble size and rate of growth were studied. It is shown that in the case of drastic pressure differentials the formation of bubbles capable of producing microcirculatory disturbances is accomplished within a few seconds.

Carbon Dioxide↗

PubMed1990

Doppler waveform pulsatility index and resistance, pressure and flow in the umbilical placental circulation: an investigation using a mathematical model.

A mathematical model of the umbilical placental circulation was used to examine the effect of different physiological variables on the pulsatility index (PI) of the umbilical artery Doppler waveform. The variables include the umbilical and placental resistances, the volume flow rate and the pressure. In the model the branching structure of the placental villous tree is considered in detail, while each arterial branch is itself represented simply using a resistor and a capacitor. Placental vascular disease is modelled as obliteration of a fraction of the terminal branches of the tree. The model umbilical artery PI depends on the ratio of the placental resistance to the umbilical artery resistance. The PI increases with vascular disease, but the rate of increase is not uniform. Initially, the placental resistance and the PI increase very slowly with vessel obliteration. Once the level of vessel obliteration has reached a large enough value--typically between 60% and 90% obliteration--the PI begins to rise sharply. A larger placental vascular bed can accommodate a greater level of vessel obliteration before this rapid PI rise begins. The umbilical artery PI also depends on the pulsatility of the input (aortic bifurcation) pressure waveform, but blood pressure variations in the physically attainable range cannot account for the very high PI values associated with fetal compromise. Physically attainable pressure waveform changes would, however, enable the fetus with substantial placental vascular disease to maintain umbilical volume flow rate, and at the same time exhibit a raised umbilical artery PI value.

Blood Flow Velocity↗

PubMed1988

Interrelations between glycolysis and the hexose monophosphate shunt in erythrocytes as studied on the basis of a mathematical model.

A mathematical model is presented which comprises the reactions of glycolysis, the hexose monophosphate shunt (HMS) and the glutathione system in erythrocytes. The model is used to calculate stationary and time-dependent metabolic states of the cell in vitro and in vivo. The model properly accounts for the following metabolic features observed in vitro: (a) stimulation of the oxidative pentose pathway after addition of pyruvate due to a NADP-dependent lactate dehydrogenase as coupling enzyme between glycolysis and the oxidative pentose pathway, (b) relative share of the oxidative pentose pathway in the total consumption of glucose amounting to approximately 10% in the normal case and to approximately 90% under conditions of oxidative stress excreted by methylene blue. From the application of the model to in vivo conditions it is predicted that (c) under normal conditions glycolysis and the HMS are independently regulated by the energetic and oxidative load, respectively, (d) under conditions of enhanced energetic or oxidative load both glycolysis and the HMS are mainly controlled by the hexokinase; in this situation the highest possible values of the energetic and oxidative load which are compatible with cell integrity are strongly coupled and considerably restricted in comparison with the normal case, (e) the stationary states possess bifurcation points at high and low values of the energetic load.

Energy Metabolism↗

PubMed1989

Cost-benefit analysis of tetanus prophylaxis by a mathematical model.

A mathematical model has been developed which allows estimation of the epidemiological and economic effects of different tetanus vaccination strategies. The model was used to simulate the epidemiology of tetanus in Italy from 1955 to 1982, and then applied to a district of Tuscany by utilizing data obtained from a seroepidemiological survey carried out in the same area. For this district we simulated vaccination programmes designed to reach, within 1 or 10 years, coverages of 60 or 90% of the population aged over 10 years who had not been exposed to the neonatal vaccination programme. The most effective strategy, from both the epidemiological and economic point of view, seems to be 90% coverage reached in 1 year's time. Benefits would be increased by improving the reliability of vaccinal anamnesis.

Age Factors↗

PubMed2000

Predicting and preventing measles epidemics in New Zealand: application of a mathematical model.

A mathematical model of the dynamics of measles in New Zealand was developed in 1996. The model successfully predicted an epidemic in 1997 and was instrumental in the decision to carry out an intensive MMR (measles-mumps rubella) immunization campaign in that year. While the epidemic began some months earlier than anticipated, it was rapidly brought under control, and its impact on the population was much reduced. In order to prevent the occurrence of further epidemics in New Zealand, an extended version of the model has since been developed and applied to the critical question of the optimal timing of MMR immunization.

Adolescent↗

PubMed1999

Exploration of the mechanisms of retention and clearance of low-toxicity particles in the rat lung using a mathematical model.

A mathematical model of the mechanisms of clearance or retention of inhaled particles in rat lungs is used to explore the extent to which a hypothesized sequence of events (including phagocytosis, macrophage-mediated clearance, transfer into the interstitium, transfer to lymph nodes, and overloading of the defense mechanisms) can account for data from a series of inhalation experiments with a low-toxicity, insoluble dust-titanium dioxide, TiO(2). These data include mean lung burdens and mean lymph-node burdens in groups of rats exposed to concentrations of 1, 10, 30, 50, and 90 mg m(-3), with exposure periods for as long as 2 yr (at 10 mg m(-3)), up to 7 mo at 50 mg m(-3), and 3.5 mo at 1 and 30 mg m(-3). The estimation of the parameters in the model is based mainly on information from other experimental studies or prior modeling. Values within the biologically plausible range were evaluated for the main parameters by inspection of predictions in comparison with data from the lowest concentration experiments. The suitability of the selected values was then confirmed by comparison of model predictions with data from the higher concentration experiments (at 30, 50, and 90 mg m(-3)). During inhalation, clearance rates are affected by translocation of dust and by overloading. The characterization of overload appears to describe these experiments well. Comparison with the effect of lung burden reported for other types of particles supports the hypothesis that overload is more dependent on the volume rather than the mass of the particles.

Air Pollutants↗

PubMed2001

A column study of soil contamination by lead: influence of pH and carbonate content. II. Mathematical model.

A mathematical model is used for the interpretation of the results from earlier experimental studies in lab-scale columns on the contamination of a carbonatic soil with lead. Local equilibrium conditions suffice to reproduce the experimental curves for every pH value of the influent contaminant solution and carbonate content of the soils essayed, but heterogeneous contact between the aqueous and solid phase should be included. This heterogeneous contact is responsible for the important tailing effects observed, and is difficult to estimate even for the lab conditions. Then, important uncertainties should be accepted both for risk assessment and in situ remediation feasibility studies.

Carbonates↗

PubMed1988

Noise-induced hearing damage caused by metabolic exhaustion: a mathematical model.

A mathematical model for noise-induced hearing loss is based on the assumption that hair cells are damaged, temporarily or permanently, by metabolic exhaustion, and that the number of damaged hair cells and the hearing loss are monotonically increasing functions of an energy deficiency. The purpose of the model is to focus on the influence of sound intensity, exposure duration, and temporal pattern of the sound exposure on the noise-induced hearing loss from long-duration exposures. The model is restricted to the range of sound levels where metabolic exhaustion probably is the main reason for the hair cell damage. Only exposures with similar frequency spectra and producing moderate hearing losses are considered; frequency dependence is not discussed.

Energy Metabolism↗

PubMed1998

Interaction between carotid baroregulation and the pulsating heart: a mathematical model.

A mathematical model of short-term arterial pressure control by the carotid baroreceptors in pulsatile conditions is presented. The model includes an elastance variable description of the left and right heart, the systemic (splanchnic and extrasplanchnic) and pulmonary circulations, the afferent carotid baroreceptor pathway, the sympathetic and vagal efferent activities, and the action of several effector mechanisms. The latter mechanisms work, in response to sympathetic and vagal action, by modifying systemic peripheral resistances, systemic venous unstressed volumes, heart period, and end-systolic elastances. The model is used to simulate the interaction among the carotid baroreflex, the pulsating heart, and the effector responses in different experiments. In all cases, there has been satisfactory agreement between model and experimental results. Experimental data on heart rate control can be explained fairly well by assuming that the sympathetic-parasympathetic systems interact linearly on the heart period. The carotid baroreflex can significantly modulate the cardiac function curve. However, this effect is masked in vivo by changes in arterial and atrial pressures. During heart pacing, cardiac output increases with frequency at moderate levels of heart rate and then fails to increase further because of a reduction in stroke volume. Shifting from nonpulsatile to pulsatile perfusion of the carotid sinuses decreases the overall baroreflex gain and significantly modifies operation of the carotid baroreflex. Finally, a sensitivity analysis suggests that venous unstressed volume control plays the major role in the early hemodynamic response to acute hemorrhage, whereas systemic resistance and heart rate controls are a little less important.

Animals↗

PubMed2000

Acute cardiovascular response to isocapnic hypoxia. I. A mathematical model.

A mathematical model of the acute cardiovascular response to isocapnic hypoxia is presented. It includes a pulsating heart, the systemic and pulmonary circulation, a separate description of the vascular bed in organs with the higher metabolic need, and the local effect of O(2) on these organs. Moreover, the model also includes the action of several reflex regulatory mechanisms: the peripheral chemoreceptors, the lung stretch receptors, the arterial baroreceptors, and the hypoxic response of the central nervous system. All parameters in the model are given in accordance with the physiological literature. The simulated overall response to a deep hypoxia (28 mmHg) agrees with the experimental data quite well, showing a biphasic pattern. The early phase (8-10 s), caused by activation of peripheral chemoreceptors, exhibits a moderate increase in mean systemic arterial pressure, a decrease in heart rate, a quite constant cardiac output, and a redistribution of blood flow to the organs with higher metabolic need at the expense of other organs. The later phase (20 s) is characterized by the activation of lung stretch receptors and by the central nervous system hypoxic response. During this phase, cardiac output and heart rate increase together, and blood flow is restored to normal levels also in organs with lower metabolic need. The model may be used to gain a deeper understanding of the role of each mechanism in the overall cardiovascular response to hypoxia.

Afferent Pathways↗

PubMed1996

Impairment of blood volume restitution after large hemorrhage: a mathematical model.

A mathematical model tests possible mechanisms for the progressive failure of blood volume restitution seen after larger hemorrhages ( > 26%) with increasing changes in plasma osmolality. After 10% hemorrhage, the model requires a decrease in net hydrostatic capillary pressure, the release of solute into the extracellular space, and the release of Na+ and K+ from a bound pool in equilibrium with the interstitium to match the experimental data. The solute and released cations expand the interstitium to drive the restitution of volume and protein from 3 to 24 h. After 30% hemorrhage, the best prediction of the average experimental responses occurs when the Na(+)-K(+)-adenosinetriphosphatase (ATPase) in the cell membrane is inhibited by 38.7% from 0.8 to 3 h, and the proportionality between capillary pressure and blood volume is reduced by 68% from its value for 10% hemorrhage. When the change in plasma osmolality is doubled after 30% hemorrhage, an increase in the inhibition of the ATPase to 85% and extension of its duration to 24 h are necessary to match experimental findings. The associated defect in sodium transport may occur after large hemorrhage so that sodium and water move into cells. This response may oppose osmotically driven expansion of the interstitium and thus account for the failure of restitution.

Animals↗

PubMed2000

Evaluation of intradialytic solute and fluid kinetics. Setting Up a predictive mathematical model.

A mathematical model of solute kinetics for the improvement of hemodialysis treatment is presented. It includes a two-compartment description of the main solutes and a three-compartment model of body fluids (plasma, interstitial and intracellular). The main model parameters can be individually assigned a priori, on the basis of body weight and plasma concentration values measured before beginning the session. Model predictions are compared with clinical data obtained in vivo during 11 different hemodialysis sessions performed on 6 patients with a profiled sodium concentration in the dialysate and a profiled ultrafiltration rate. In all cases, the agreement between the time pattern of model solute concentrations in plasma and the in vivo data proves fairly good as to urea, sodium, chloride, potassium and bicarbonate kinetics. Only in two sessions was blood volume directly measured in the patient, and in both cases the agreement with model predictions was good. In conclusion, the model allows a priori computation of the amount of sodium removed during hemodialysis, and makes it possible to predict the plasma volume changes and plasma osmolarity changes induced by a given sodium concentration profile in the dialysate and by a given ultrafiltration profile. Hence, it can be used to improve clinical tolerance to the dialysis session taking the characteristics of individual patients into account, in order to minimize intradialytic hypotension.

Bicarbonates↗

PubMed1986

The spread of caudal analgesia in children: a mathematical model.

A mathematical model correlating the spread of analgesia to the dose of local anaesthetic and to age or body weight was found analysing the data of 763 caudal blocks in children from age one day to twelve years. Two graphs have been plotted: (1) spread of analgesia, dose, age and (2) spread of analgesia, dose, weight. Both age and weight can be used as predictors to determine the desired level of analgesia, but weight is more useful in very young patients while age is a better guide in older children.

Aging↗

PubMedDate not supplied

[Phosphorylase kinase: mathematic modeling].

A mathematical model of the dynamic behavior of phosphorylase kinase was devised. Based on the results obtained, the function of this protein is discussed. It is suggested that phosphorylase kinase doses in a cAMP-dependent manner additional portions of glucoso-l-phosphate, which the muscle cell receives in response to contraction.

Calcium↗

PubMedDate not supplied

[Photochemiluminescent study of the antioxidant activity in biological systems. Mathematical modeling].

The mathematical modeling of the kinetics of riboflavin photo-chemiluminescence (PCL) in the presence of antioxidants, superoxide dismutase and ascorbic acid, has been performed. A specially developed computer program "Kinetic Analyzer" was used for the modeling. The PCL intensity of was taken as directly proportional to the superoxide concentration, because lucigenin had been added to the system. It was found, that the experimental curves of PCL virtually coincide with those calculated in the case of the following set of reactions (reaction rate constants, M-1.s-1 are given in brackets): hv + RH-->R. + .O2- (2,3 x 10(-4) s-1); RH + .O2(-)-->R. + H2O2 (1000); RH-->...(0,005 s-1); .O2- + .O2(-)-->... + phi OTOH (2 x 10(5) M-1 s-1); SOD + .O2(-)-->SOD H2O2 (1 x 10(8)); ASC + .O2(-)-->...(2 x 10(7)). Here RH is, .O2(-)--superoxide, R.--riboflavin radical, SOD--superoxide dismutase, ASC--ascorbate.

Ascorbic Acid↗

PubMedDate not supplied

[Isometric contractions of the myocardium: mathematic modeling].

A mathematical model describing a single contraction of a cardiac muscle strip under isometric conditions is proposed. The adequacy of the model was checked in experiments on cardiac strips from patients with chronic coronary insufficiency. It was shown that the contraction-relaxation cycle is rather completely characterized by the parameters characterizing the association-dissociation kinetics of actomyosin bridges.

Humans↗

PubMedDate not supplied

[Electron and proton transport in chloroplasts taking into account lateral heterogeneity of thylakoids. Mathematical model].

A mathematical model of a chloroplast was constructed, which takes into account the inhomogeneous distribution of complexes of photosystems I and II between granal and intergranal thylakoids. The structural and functional complexes of photosystems I and II, which are localized in intergranal and granal thylakoids, respectively, and the b/f complex, which is uniformly distributed in thylakoid membranes, are assumed to be immobile. The interactions between spatially distant electron transport complexes are provided by plastoquinone and plastocyanine, which diffuse in the thylakoid membrane and intrathylakoid space, respectively. The main stages of proton transport associated with the functioning of photosystem II and oxidation-reduction transformations of plastoquinone are considered. The model takes into account the interactions of protons with membrane-bound buffer groups, the lateral diffusion of hydrogen ions in the intrathylakoid space and in the lumen between adjacent granal thylakoids, and the transmembrane proton transport associated with the function of ATP synthase and passive leakage of protons from thylakoids outside. The numerical integration of two systems of differential equations describing the behavior of some variables in two different regions: granal and intergranal thylakoids was performed. The model describes adequately the kinetics of processes being studied and predicts the occurrence of inhomogeneous lateral profiles of proton potentials and redox state of electron carriers. Modeling the electron and proton transport with allowance for the topological features of chloroplasts (lateral heterogeneity of thylakoids) is important for correct interpretation of "power-flux" interactions and the experimentally measured kinetic parameters averaged over the entire spatially inhomogeneous thylakoid system.

Biological Transport↗

PubMed1994

The effect of blood volume loss on cardiovascular response to lower body negative pressure using a mathematical model.

Different mathematical models of varying complexity have been proposed in recent years to study the cardiovascular (CV) system. However, only a few of them specifically address the response to lower body negative pressure (LBNP), a stress that can be applied in weightlessness to predict changes in orthostatic tolerance. Also, the simulated results produced by these models agree only partially with experimental observations. In contrast, the model proposed by Melchior et al., and modified by Karam et al. is a simple representation of the CV system capable of accurately reproducing observed LBNP responses up to presyncopal levels. There are significant changes in LBNP response due to a loss of blood volume and other alterations that occur in weightlessness and related one-g conditions such as bedrest. A few days of bedrest can cause up to 15% blood volume loss (BVL), with consequent decreases in both stroke volume and cardiac output, and increases in heart rate, mean arterial pressure, and total peripheral resistance. These changes are more pronounced at higher levels of LBNP. This paper presents the results of a simulation study using our CV model to examine the effect of BVL on LBNP response.

Blood Pressure↗