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PubMed1995

Maximum expiratory flow-volume curve: mathematical model and experimental results.

A mathematical simulation of the maximum expiratory flow-volume (MEFV) curve was developed using a lumped parameter model. The model uses a theoretical approximation of an activation function representing the lung's pressure-volume relationship during maximally forced expiration. The waveforms obtained by the model were compared to the flow-volume curves recorded from normal subjects and for patients with small airways disease, asthma, and emphysema. We were able to reproduce the flow-volume curves using the model and calculate new parameters that reflect the dependency of airways resistance on expired volume during FVS manoeuvre. These new parameters are based on the entire information presented in the flow-volume curve and on the reduction in flow at all lung volumes. We also calculated the mean slope of the resistance-expired volume curves obtained from the model by fitting a straight line to the curve. Using representative data for normal and COPD patients different mean slopes of 0.095, 0.13, 0.49 and 1.44 litre-1 were obtained for normal subject, small airways disease, asthma and emphysema patients, respectively. The model-based parameters may be applicable to human studies. However, further studies in large groups of patients are required to better define the true predictive value of the new indices described for the diagnosis of COPD.

Asthma↗
PubMed1983

A simple mathematical model for predicting lithium dose requirement.

Available methods of predicting lithium dose have been based on kinetics of a single test dose. A statistically based mathematical model was developed in which lithium dose is derived by stepwise multiple linear regression based on desired level, form of lithium, concomitant tricyclic use, age, sex, and weight. Predictions of the model were correct to within 300 mg in 66% of the 100 initial cases and within 600 mg in 94% of cases. A validation study of 112 additional cases revealed similar percentage. The simple mathematical expression derived from record review allows the clinician to calculate the relationship of steady-state lithium dosage to serum level prior to initiating treatment.

Adult↗
PubMed1990

A mathematical model of erythropoiesis suggests an altered plasma volume control as cause for anemia in aged mice.

In order to evaluate whether the anemia observed in aged C57B1 and B6D2F1 mice reflects a defect in the control mechanisms regulating erythropoiesis a mathematical model of erythropoietic control is employed, validated previously. In the model it is hypothesized that the most important mechanism for compensating an actual demand of red blood cells is an increase in the mitotic amplification (number of mitoses) of erythroid progenitors (CFU-E, erythroblasts). The same sigmoidal dose-response-relationship between mitotic amplification and hematocrit (Hct) is proposed for young and aged mice. It is mediated by erythropoietin (EPO). Using this relationship one can demonstrate that the expansion of the plasma volume (PV) observed in aged mice is appropriately compensated by an increase in the mitotic amplification of CFU-E and erythroblasts. This implies that aged mice operate in a stimulated state of erythropoietic amplification which is closer to the maximum of the dose-response-relationship than the steady state in young mice. This explains the finding of a reduced proliferative reserve in aged mice following further erythropoietic stimulation. An additional analysis regarding the response of aged mice to bleeding anemia is consistent with the view that young and aged mice share the same dose-response-relationship but start from different steady states. These findings suggest that the control mechanisms regulating erythropoiesis in young and aged mice are similar and that the anemia is due to alterations in the PV control.

Animals↗
PubMed2002

A mathematical model for pattern of change in beta-cell reserve and factors affecting residual reserve within the first 2 years of type 1 diabetes.

The aim of this study was to investigate the effects of age, duration of diabetes, sex and ICA (Islet cell cytoplasmic antibody) on beta-cell reserves and to develop a model within the first 2 years of Type 1 diabetes. Beta-cell reserve is evaluated as fasting (FCp) and 1 mg i.v. glucagon stimulated C-peptide (SCp) levels in 58 Type 1 diabetics and in 12 normoglycemic subjects. Patients were divided into 3 groups according to duration of diabetes: Group I (2.5+/-0.3 weeks), Group II (13.4+/-1.2 months) and Group III (24.2+/-1.8 months). FCp/SCp level in nmol/l (mean+/-SE) were as follows. Group I: 0.21+/-0.02/0.38+/-0.04, Group II: 0.15+/-0.01/0.27+/-0.02, Group III: 0.07+/-0.01/0.11+/-0.02, CONTROL GROUP: 0.42+/-0.09/1.29+/-0.13. The scatter plots of C-peptide levels vs time in all the diabetic patients fitted in to a 4th-order polynomial regression (R: 0.96-0.98). Age was strongly correlated with FCp (rs: 0.46, p<0.05) and ICA positivity affected Cp-levels negatively (p>0.05). In conclusion, as the duration of diabetes increases, response time to glucagon prolongs and amplitude of it shortens. Duration of diabetes of less than 2 weeks, feminity, puberty and ICA positivity affect beta-cell reserve negatively, conversely, masculinity, post-puberty, older age and ICA negativity affect the reserve positively. The dynamics of C-peptide response to glucagon follow a mathematical model and Type 1 diabetes causes a decrease not only in the amplitude of the response but also in the duration of the response.

Adolescent↗
PubMed2005

[Tendency and mathematical model of relationship of blood ATP content with temperature and time of preservation].

To investigate the relationship of blood ATP content with temperature and time of preservation and to establish its mathematical model, adenosine triphosphate (ATP) concentration was applied as the index of the quality of erythrocytes; systematical study on variation of blood preserved in a series of different temperatures from 4 degrees C to 32 degrees C was performed, and a series of experimental data were obtained. The results showed that when the ATP concentration y = f (d, t, s) in preserved blood was given as the continuous function of the time (d), the temperature (t) and the initiate ATP concentration (s), the model was fitted with the theory of linearity regression in symbolic statistics, and the general mathematical physical equation of the variation of preserved blood quality was deduced. According to the equation, the whole blood in CPDA-1 solution could be efficiently stored for 35, 35, 29, 22, 18, 18, 13, 8, 7, 6, 6, 5, 4, 4 and 3 days in 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 and 32 degrees C, respectively. In conclusion, the general tendency of the variation of preserved blood quality according to the temperature and the time was systematically disclosed for the first time, which would be propitious to estimate the blood quality in various temperatures and to instruct clinical blood transfusion.

Adenosine Triphosphate↗
PubMedDate not supplied

Mathematical models of disease transmission: a precious tool for the study of sexually transmitted diseases.

This paper is an introduction to the mathematical epidemiology of sexually transmitted diseases (STDs) and its application to public health. After a brief introduction to transmission dynamics models, the construction of a deterministic compartmental mathematical model of HIV transmission in a population is described. As a background to STD transmission dynamics, basic reproductive rate, intergroup mixing, rate of partner change, and duration of infectivity are discussed. Use of the models illustrates the effect of sexual mixing (proportionate to highly assortative), of preventive intervention campaigns, and of HIV-chlamydia interaction on HIV prevalence in the different population groups. In particular, planned prevention campaigns can benefit the targeted intervention group but surprisingly can be disadvantageous for the general population. Through examples, mathematical models are shown to be helpful in our understanding of disease transmission, in interpretation of observed trends, in planning of prevention strategies, and in guiding data collection.

Adult↗
PubMed1997

Feasibility of mathematical models to predict success in video-assisted thoracic surgery lung nodule excision.

BACKGROUND: Pulmonary nodules are occasionally difficult to excise using video-assisted thoracic surgery (VATS). METHODS: To predict operative success, mathematical models using preoperative computerized tomography (CT) measurements were tested in 50 consecutive patients who underwent attempted or successful thoracoscopic lung biopsy. Unrelated technical problems resulted in the exclusion of 3 patients. RESULTS: No differences were noted with respect to lobar location, thoracic dimensions, gender, presence of chronic obstructive pulmonary disease, or nodule pathology. The expression S/(D + 1), where S = nodule size (cm) and D = distance (cm) to the nearest visceral pleura, yielded significantly higher values for visible nodules (P < 0.001). Resectable nodules had a higher score using the expression 1/(S + D + 1), (P < 0.001). Simple cases (n = 19) were defined as those in which nodules were both visible and resectable with very basic VATS techniques. All others (n = 28) were considered complex. The derived expression for Simplicity [1/(S(D + 1))] yielded significantly higher values for simple cases (0.8 +/- 0.3 vs. 0.3 +/- 0.2 cm(-2), P < 0.001) and all simple cases had a score > or = 0.4. Logistic regression analysis showed that the formulas for resectability and simplicity were significant independent predictors for resectability and simplicity. CONCLUSIONS: Equations based on objective CT measurements may be useful for planning VATS nodulectomy or studying the outcome of these minimally invasive operations.

Feasibility Studies↗
PubMed2003

Eye-head coordination in darkness: formulation and testing of a mathematical model.

Passive head rotation in darkness produces vestibular nystagmus, consisting of slow and quick phases. The vestibulo-ocular reflex produces the slow phases, in the compensatory direction, while the fast phases, in the same direction as head rotation, are of saccadic origin. We have investigated how the saccadic components of the ocular motor responses evoked by active head rotation in darkness are generated, assuming the only available sensory information is that provided by the vestibular system. We recorded the eye and head movements of nine normal subjects during active head rotation in darkness. Subjects were instructed to rotate their heads in a sinusoidal-like manner and to focus their attention on producing a smooth head rotation. We found that the desired eye position signal provided to the saccadic mechanism by the vestibular system may be modeled as a linear combination of head velocity and head displacement information. Here we present a mathematical model for the generation of both the slow and quick phases of vestibular nystagmus based on our findings. Simulations of this model accurately fit experimental data recorded from subjects.

Adult↗
PubMed1992

[A mathematical model of the vascular architecture and of the distribution of resistances in the coronary tree].

The architecture and resistance distribution of the coronary arteriolar tree downstream 100 mu diameter vessels are still largely unknown, due to technical difficulties in direct visualization. In this study we propose a mathematical model of the architecture and the single vessel resistance distribution of terminal arteriolar vasculature in the beating dog heart, based on the analysis of embolization-induced changes of total coronary resistance. Coronary embolization was performed by injecting several boluses of 15 mu (6 cases) and 25 mu (6 cases) plastic microspheres into the maximally vasodilated (adenosine infusion) left circumflex artery of the open chest dog. The relation between the number of plastic beads progressively injected to embolize 15 mu and 25 mu vessels and the resulting increase in total coronary resistance (occlusion function) was obtained in each experiment. If we consider a binary symmetric vascular tree with i) equal resistance for vessels of the same branching order and ii) optimal ratio between resistance of parent and daughter vessels at all branching sites, the simulation of embolization in such a system shows that the occlusion function of the terminal vessels N in the linear portion between 0 and N/2 occluded vessels has a slope S' which is 5.6 times lower than the slope S" between N/2 and 3/4 N occluded vessels and 3.6 times lower than the S' of the occlusion function of the preterminal vessels. The occlusion function in our experiments has a ratio S"/S' close to that predicted by the model and a ratio between the S' of the 25 mu and that of 15 mu experiments equal to 4.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed2007

Effect of ferrous ion on the biological activity in a UASB reactor: mathematical modeling and verification.

The effect of ferrous ion on the biological activity in a upflow anaerobic sludge blanket (UASB) reactor was studied. A mathematical model was developed and validated in order to simulate the dynamic behavior of a UASB reactor. This model took into consideration of all the biological and physicochemical reactions. The model was able to simulate the accumulation of iron in the sludge bed and its effect on the biological activity of the anaerobic sludge. A significant increase in the maximum uptake rate of methanogens and acidogens was revealed when iron was supplemented to the UASB reactor. The addition of ferrous iron induced a stable and excellent COD conversion rate. The model can be a useful tool for the prediction of process performance in the future and can be used to assist in the operation of biogas plants. The ferrous ion addition proved to enhance the biological activity of UASB sludge. Thus, the model can be used for the design of treatment plants that will take advantage of the benefits of iron addition.

Anaerobiosis↗
PubMed2000

Effects of antiviral usage on transmission dynamics of herpes simplex virus type 1 and on antiviral resistance: predictions of mathematical models.

Herpes simplex virus type 1 (HSV-1) causes recurrent herpes labialis (RHL), a common disease afflicting up to 40% of adults worldwide. Mathematical models are used to analyze the effect of antiviral treatment on the transmission of, and the prevalence of drug resistance in, HSV-1 in the United States. Three scenarios are analyzed: no antiviral use, the current level of use, and a substantial increase in nucleoside analogue use, such as might occur if topical penciclovir were available over-the-counter for the treatment of RHL. A basic model predicts that present level of nucleoside analogue use has a negligible effect on HSV-1 transmission and that even if use of topical penciclovir for (RHL) increased substantially, the overall prevalence of infectious HSV-1 is unlikely to be reduced by more than 5%. An expanded model, which allows for acquired resistance and includes immunocompromised hosts and other more realistic features, predicts that current antiviral use is unlikely to lead to any noticeable increase in resistance. If antiviral use increases, the resulting rise in resistance in the population will depend primarily on the probability that immunocompetent hosts will acquire permanent resistance upon treatment. This probability is known to be small, but its exact value remains uncertain. If acquired resistance occurs less than once per 2,500 treated episodes, then in the community at large, the frequency of HSV-1 resistance is predicted to increase slowly, if at all (remaining below 0.5% for >50 years), even with extensive nucleoside analogue use. If acquired resistance emerges in 1 of 625 treated episodes (the maximum of an approximate 95% confidence interval derived from the results of several studies of resistance in treated hosts), then the prevalence of infection with resistant HSV-1 could rise from about 0.2% to 1.5 to 3% within 50 years. The limitations of existing data on acquired resistance and the potential impact of acquired resistance if it occurs are discussed, and strategies are suggested for enhancing information on acquired resistance. The predictions of this model contrast with the more rapid increases in antimicrobial resistance anticipated by models and observed for other pathogenic bacteria and viruses. The reasons for these contrasting predictions are discussed.

Aging↗
PubMed1997

Comparison of a mathematical model to predict 10-km performance from the Conconi test and ventilatory threshold measurements.

The purpose of this study was to validate a mathematical model (MM) that evaluates the Conconi test and predicts 10-km race time. In addition, the relationship between ventilatory threshold (Tvent) determined from a laboratory test and heart rate deflection (HRd) from the Conconi test were examined. Seventeen trained runners performed the Conconi test, and performance times were predicted using a MM based on a logistics function. A correlational analysis indicated a highly significant relationship (r = .98, p < .01) between MM predicted time and actual time. Significant relationships were found between velocity at Tvent and HRd (r = .95, p < .01), and predicted times from each method (r = .96, p < .01). Heart rates from Tvent and HRd were also related (r = .79, p < .01). These results suggest that a MM of the Conconi test is a valid method of predicting 10-km performance and is closely related to traditional laboratory measures.

Adult↗
PubMed2005

Mathematical models of oxygen and carbon dioxide storage and transport: interstitial fluid and tissue stores and whole-body transport.

This article describes a mathematical model of whole-body O2 and CO2 transport. The model includes representation of the acid-base chemistry of the blood, interstitial fluid, and tissues, plus transport of O2 and CO2 between compartments representing tissues, interstitial fluid, arterial and venous blood, and lungs. The model includes equations for calculation of all concentrations in the compartments, including equations describing the physicochemical properties and reaction equations of interstitial fluid and tissues. In addition, the model includes equations that describe the flow of substrate between the compartments and differential equations allowing calculation of the changes in state variables caused by the flow of substrates between the compartments. This model is designed to calculate the effects of metabolic and respiratory perturbations, such as variation in breathing pattern or production of strong acid at the tissues. The model reproduces the results of published experiments when used to simulate (1) normal conditions in the lungs, arterial and venous blood, interstitial fluid, and tissues during normal ventilation; (2) the characteristic two-exponential response to changes in minute ventilation; and (3) the relationship between arterial blood values of PCO2 and HCO3,p during inspiration of different fractions of CO2.

Acid-Base Equilibrium↗
PubMedDate not supplied

[Mathematical model of the interaction of components in a plant-rhizospheric microorganisms system at the higher level of carbon dioxide in atmosphere].

A mathematical model describing the interaction of plants and rhizospheric microorganisms on complete mineral medium at a higher CO2 level in the atmosphere was constructed. The positive effect of CO2-enrichment on the system plant--rhizospheric microorganisms was shown. The effect of rhizospheric microorganisms on plant growth at normal and high level of carbon dioxide was demonstrated. It was shown that the biomass of plant in the system is smaller than the biomass of plant growing without microorganisms. It was experimentally demonstrated that a simple ecosystem wheat--Pseudomonas putida--artificial soil develops and functions differently than its individual constituents in the case of a wheat-artificial soil system. With unlimited nutrition and a higher CO2 level (0.06%), plants with roots inoculated with microorganisms have a smaller biomass than plants that were not inoculated with microorganisms.

Algorithms↗
PubMed2003

[Effects of the oxygen partial pressure in inspired gaseous mixture on the functional state of the circulatory, respiratory and erythropoietic systems: a mathematical model].

Oxygen partial pressure in inspired gaseous mixture has a profound effect on the function of the circulatory, respiratory and erythropoietic systems. A mathematical model is proposed to optimize the function of these systems when breathing air with various PO2. The model is based on the principle of minimum energy expenditure. Erythrocyte count, arterial oxygen tension, cardiac output, and pulmonary ventilation are determined as a function of inspired PO2. The model results are in good agreement with the data for permanent altitude residents.

Blood Circulation↗
PubMed1987

Mathematical model of Klebsiella pneumoniae resistance to amikacin and gentamicin.

1. The resistance of Klebsiella pneumoniae to amikacin and gentamicin was studied by a mathematical model to predict the rate of sensitivity decrease. The results accurately matched experimental data, showing that the model is a reliable predicting tool. 2. The observations were carried out over six years and included 2677 cultures that were positive for K. pneumoniae. At the beginning of the observation period, 85.7% of the cultures were sensitive to amikacin and 40.8% were sensitive to gentamicin. Sensitivity to amikacin showed a surprisingly rapid decrease; at the end of the experimental period, amikacin and gentamicin sensitivities were 33.3% and 27.8%, respectively. 3. We conclude that patterns of resistance of other bacteria could be investigated using this method.

Amikacin↗
PubMed2006

Mathematical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview.

We report a major project to develop integrated mathematical models for predicting the epidemiologic and economic effects of malaria vaccines both at the individual and population level. The project has developed models of the within-host dynamics of Plasmodium falciparum that have been fitted to parasite density profiles from malaria therapy patients, and simulations of P. falciparum epidemiology fitted to field malariologic datasets from a large ensemble of settings across Africa. The models provide a unique platform for predicting both the short- and long-term effects of malaria vaccines on the burden of disease, allowing for the temporal dynamics of effects on immunity and transmission. We discuss how the models can be used to obtain robust cost-effectiveness estimates for a wide range of malaria vaccines and vaccination delivery strategies in different eco-epidemiologic settings. This paper outlines for a non-mathematical audience the approach we have taken and its underlying rationale.

Animals↗
PubMed1976

Particle size-shape distributions: the general spheroid problem. I. Mathematical model.

The development of stereological methods for the study of dilute phases of particles, voids or organelles embedded in a matrix, from measurements made on plane or linear intercepts through the aggregate, has deserved a great deal of effort. With almost no exception, the problem of describing the particulate phase is reduced to that of identifying the statistical distribution--histogram in practice--of a relevant size parameter, with the previous assumption that the particles are modelled by geometrical objects of a constant shape (e.g. spheres). Therefore, particles exhibiting a random variation about a given type of shape as well as a random variation in size, escape previous analyses. Such is the case of unequiaxed particles modelled by triaxial ellipsoids of variable size and eccentricity parameters. It has been conjectured (Moran, 1972) that this problem is indetermined in its generally (i.e. the elliptical sections do not furnish a sufficient information which permits a complete description of the ellipsoids). A proof of this conjecture is given in the Appendix. When the ellipsoids are biaxial (spheroids) and of the same type (prolate or oblate), the problem is identifiable. Previous attempts to solve it assume statistical independence between size and shape. A complete, theoretical solution of the spheroids problem--with the independence condition relaxed--is presented. A number of exact relationships--some of them of a striking simplicity--linking particle properties (e.g. mean-mean caliper length, mean axial ratio, correlation coefficient between principal diameters, etc.) on the one hand, with the major and minor dimensions of the ellipses of section on the other, emerge, and natural, consistent estimators of the mentioned properties are made easily accessible for practical computation. Finally, the scope and limitations of the mathematical model are discussed.

Mathematics↗