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Results for “mathematical modelling”

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PubMed2005

Synchronization of oscillations of proliferation of keratinocytes in psoriatic skin by external periodic force: a mathematical model.

A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear differential equations. Its qualitative analysis was carried out and numerical solutions were obtained at the parameter values corresponding to these states. It was shown that in the norm, a single stable equilibrium of a "focus" type exists in the system; whereas in psoriasis, owing to an increase in the growing fraction, hyperproliferation, and enhanced migration of interacting keratinocytes, a stable limit cycle arises from the state of unstable focus. In this paper we also report on the results of computer modeling of synchronization of self-excited oscillations of keratinocyte population density in psoriatic lesions by an external periodic force. This synchronization is viewed as a possible mechanism of the clinically observed dependence of psoriasis course on some natural factors of cyclic nature.

Cell Proliferation↗

PubMed2004

A study on pesticide runoff from paddy fields to a river in rural region--2: development and application of a mathematical model.

A mathematical model was developed to predict the runoff of pesticides from paddy fields to a river in a rural region. The model comprises three submodels: (1) submodel for river flow, (2) submodel for pesticide behavior in paddy fields, (3) submodel for pesticide behavior in a river. The tank model was applied to predict the river flow and the paddy water. In order to reproduce the actual behavior of pesticides in paddy fields, the kinetics of the transport and reaction mechanisms of pesticides applied to paddy fields were considered in the model. The model was applied to the Kozakura River Basin where the detailed field survey was conducted. The model reflected well the runoff characteristics of pesticides obtained from the detailed field survey.

Agriculture↗

PubMed2003

Deciphering environmental signal integration in sigma54-dependent promoters with a simple mathematical model.

A mathematical model was developed to describe the physiological co-regulation of two Pseudomonas sigma54-dependent promoter/regulator systems, Pu/XylR and Po/DmpR of Pseudomonas strains mt2 and CF600, respectively. Five ordinary differential equations and six algebraic equations were developed to describe the following processes of transcription initiation: binding of the activator protein to the upstream activating sequence, union of the sigma factor with the core polymerase, formation of the open complex, and escape of the transcription machinery from the promoter region. In addition, growth-phase control of the integration host factor (IHF), sigma-70 regulation during stationary phase, and the contribution of (p)ppGpp to both sigma factor selectivity and promoter escape were hypothesized. By including any three of these four effects, the model predicted that expression from both promoters is repressed during exponential growth and sharply increases as the cells enter stationary phase. The difference in behavior of the two systems during overexpression of either sigma54 or (p)ppGpp could be explained by different values of two model parameters. To accurately represent the behavior of both promoters in (p)ppGpp null strains, an additional parameter must be varied. Although numerical data available for this system is scarce, the model has proved useful for helping to interpret the experimental observations and to evaluate four hypotheses that have been proposed to explain the phenomenon of exponential silencing.

Bacterial Proteins↗

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↗

PubMed2004

Towards optimal regimens for the UVB phototherapy of psoriasis: a mathematical model.

A mathematical model is described that predicts the response of psoriasis to a treatment course of UVB irradiation. The basis of the model is that UVB acts by a direct effect on keratinocytes and that cell cycle arrest is the major mode of action in the phototherapeutic response in psoriasis. Although it is unlikely that UVB causes resolution of psoriatic plaques through a single mechanism, the current model has been based on epidermal cell cycle arrest and entry into the terminal differentiation compartment because this is likely to be a significant rate-limiting factor in determining response to treatment. The model has been validated against results obtained from published clinical studies on narrowband (TL-01) UVB phototherapy for psoriasis. The principal outcomes of the model are that for a given erythemal response, the number of exposures required for clearance is almost independent of the frequency with which patients attend for treatment and that the higher the exposure dose per treatment, the more rapidly will clearance result. The model has been used to suggest optimal regimens for the treatment of outpatients and inpatients.

Cell Division↗

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↗

PubMed1983

Temperature dependence of vegetative growth and dark respiration: a mathematical model.

A mathematical model of the processes involved in carbon metabolism is described that predicts the influence of temperature on the growth of plants. The model assumes that the rate of production of dry matter depends both on the temperature and the level of nonstructural carbohydrate. The level of nonstructural carbohydrate is determined by the rates of photosynthesis, growth, and maintenance respiration. The model describes the rate of growth and dark respiration, and the levels of carbohydrate seen in vegetative growth of carnation and tomato. The model suggests that the growth of plants at low temperatures is limited by a shortage of respiratory energy, whereas at high temperatures growth is limited by the shortage of carbohydrate. Thermoperiodism, wherein a warm day and cool night results in faster growth than does constant temperature, is explained by the model as an increase in the level of nonstructural carbohydrate which promotes the rate of growth relative to the rate of maintenance respiration.

Journal Article↗

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↗