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At least 1,675 records · Page 93Linked to original sources
PubMed1993

Mathematical modelling of the human cardiovascular system in the presence of stenosis.

This paper reports a theoretical study on the distribution of blood flow in the human cardiovascular system when one or more blood vessels are affected by stenosis. The analysis employs a mathematical model of the entire system based on the finite element method. The arterial-venous network is represented by a large number of interconnected segments in the model. Values for the model parameters are based upon the published data on the physiological and rheological properties of blood. Computational results show how blood flow through various parts of the cardiovascular system is affected by stenosis in different blood vessels. No significant changes in the flow parameters of the cardiovascular system were found to occur when the reduction in the lumen diameter of the stenosed vessels was less than 65%.

Blood Circulation↗
PubMed1995

A mathematical model for predicting the temperature distribution in laser-induced hyperthermia. Experimental evaluation and applications.

A time-dependent mathematical model for the heat transfer in laser-induced hyperthermia has been developed. The model calculates the temperature distribution in surface-irradiated tissues. Good agreement was found between the predictions of the model and in vitro experimental results obtained for bovine liver irradiated with an expanded beam from a Nd:YAG laser. Surface evaporation of water was included in the model and experimentally verified. The discrepancy between the measured and the calculated rise in temperature at three different depths on the axis of symmetry of the irradiating beam was found to be less than 5% after 15 min of irradiation. When irradiating in air and not accounting for the surface evaporation in the model, the accuracy of the model predictions was only 75-80%. The model was then used to investigate the influence of surface evaporation of water on the total temperature distribution theoretically in a clinically relevant case. From the numerical simulations, it was shown that, simply by providing a moistened liver surface, the maximum steady-state temperature could be forced into the tissue to a depth of 4 mm. It was also shown that, by employing the numerical model during the initial phase of hyperthermia treatment, overshooting of the temperature during the transient thermal build-up time could be prevented.

Animals↗
PubMed1997

Mathematical description of photobleaching in vivo describing the influence of tissue optics on measured fluorescence signals.

The observed decrease in the fluorescence signal during photodynamic therapy (PDT) may contain dosimetric information as this photobleaching provides direct information on the photodynamic processes occurring in the tissue. A correct interpretation of the photobleaching signal, however, is crucial for its use in dosimetry. In this study the influence of scattering and absorption phenomena in tissue on the emitted fluorescence signal are described mathematically. Analytical solutions of the resulting expression show a difference from the single-decaying-exponential function generally used for describing photobleaching signals. The solutions are a function of the fluence rate at the inner side of tissue boundary psi(0*), the photobleaching dose constant beta, the incident irradiation power I0 and time. The accuracy of the results was investigated by comparison of the analytic solutions with numerical calculations using fluence rate profiles and escape functions obtained by Monte Carlo (MC) simulations. Good resemblance is observed when the value for psi(0*) calculated by the MC simulations is used in the analytical solutions. Experimental results in this study indicate the photobleaching dose constant of ALA-induced PpIX to be 33 +/- 3 J cm-2. Determination of beta for different types of photosensitizer and the development of an accurate method to determine psi(0*) can make monitoring of photobleaching during PDT valuable for dosimetry.

Aminolevulinic Acid↗
PubMed1998

Mathematical model of the CA1 region of the rat hippocampus.

A mathematical transcription of the intrinsic circuit of the CA1 region of the rat dorsal hippocampus was made and the model parameters adjusted according to experimental data from intracellular recordings and single channel kinetics. This model was able to simulate well the profile of the field potentials recorded extracellularly and the well known phenomenon of the paired-pulse depression. The results suggest that the depression of the second pulse, often interpreted in the literature as resulting from GABA(A) inhibition, can also be due to 'shunting' effects on the CA1 pyramids' membrane. The rhythmic oscillations of the field potential (EEG) was obtained as an emergent property of the network dynamics. The frequency of the field oscillation followed the main synaptic input in the region (Schaffer collaterals).

Animals↗
PubMed1991

A mathematical model of some aspects of jet nebuliser performance.

A simple mathematical model describing the performance of an Acorn jet nebuliser system (Medic-Aid Ltd) has been developed in which nebuliser efficiency E, defined as the volume fraction of solution (water) released as an aerosol or lost by evaporation, and nebulisation time T, are given as functions of the initial volume of solution. The model identifies an initial phase during which the nebuliser output is at a constant, continuous rate of 0.007 ml s-1. This is followed by an intermittent phase of operation during which output is estimated to occur for 0.25 of the total duration of the phase and results from solution deposited on the walls being recycled. The model indicates that increasing the flow of solution to the nebulisation region in the nebuliser or decreasing the fraction of aerosol intercepted by the baffle, will decrease T whilst leaving E unaffected. Two residence times tau 1, tau 2 which are a measure of the time that solution droplets adhere to the inner walls of the nebuliser are also identified; tau 1 (= 1.6 s) is the residence time associated with the rapid recycling of the majority (a fraction eta 1 = 0.992) of the aerosol while tau 2 (= 200 s) the residence time associated with the remaining fraction 1 - eta 1. Increasing eta 1 will increase E for constant tau 1, tau 2 while increasing tau 1, tau 2 will decrease E, T remaining essentially unchanged. It is proposed that the model may be applicable to other jet nebulisers.

Aerosols↗
PubMed1995

Modal and temporal analysis of head mathematical models.

The basic hypotheses used during these investigations were based on the vibration analysis of the head, which demonstrated that the head is not a solid nondeformable body, but a complex structure including deformable elements. Laboratoire des Systemes Biomecanique (LSBM) has recently proposed three mathematical models: a lumped model, a finite element model of the head in its sagittal plane, and a three-dimensional finite element model. These models were validated by their modal behavior and enabled the lesion mechanisms to be distinguished as a function of the spectral characteristics of the shock. The objective of this study is to complete these modal results by temporal analysis of the models by calculating the evolution of the intracranian mechanical parameters under shock conditions. To describe the head's dynamic behavior in the temporal domain, constant energy shocks of variable duration were simulated to evaluate their influence on different quantities as the intracerebral stresses in terms of compression, tensile, and shearing stresses, the relative brain-skull displacement, and the skull deformation. The importance of modal behavior of the head is illustrated by analyzing its temporal response to variable duration impacts, thus exciting very different frequencies. For a triangular shock, the critical duration times are between 10 and 15 x 10(-3) s, which correspond to impacts that excite the first resonance frequency of the head. Taking modal behavior into consideration in developing the finite element model leads to a harmonization of the calculated intracerebral stresses, even for short duration shocks. So, when the head is considered as a complex structure made up of several deformable elements, risk limitation is conditioned by an impact energy reduction for frequencies close to the natural frequencies of the structure. In the time field, the objective will be to avoid a number of impact shapes and durations. Therefore, the aim will not be to dampen the impact at any cost, but to damper it in an "intelligent" manner. In the future, this will allow the reduction of an injury mechanism-related risk, without increasing the risk of an injury generated by another mechanism.

Biomechanical Phenomena↗
PubMed2002

Testing a mathematical model of the yeast cell cycle.

We derived novel, testable predictions from a mathematical model of the budding yeast cell cycle. A key qualitative prediction of bistability was confirmed in a strain simultaneously lacking cdc14 and G1 cyclins. The model correctly predicted quantitative dependence of cell size on gene dosage of the G1 cyclin CLN3, but it incorrectly predicted strong genetic interactions between G1 cyclins and the anaphase-promoting complex specificity factor Cdh1. To provide constraints on model generation, we determined accurate concentrations for the abundance of all nine cyclins as well as the inhibitor Sic1 and the catalytic subunit Cdc28. For many of these we determined abundance throughout the cell cycle by centrifugal elutriation, in the presence or absence of Cdh1. In addition, perturbations to the Clb-kinase oscillator were introduced, and the effects on cyclin and Sic1 levels were compared between model and experiment. Reasonable agreement was obtained in many of these experiments, but significant experimental discrepancies from the model predictions were also observed. Thus, the model is a strong but incomplete attempt at a realistic representation of cell cycle control. Constraints of the sort developed here will be important in development of a truly predictive model.

CDC28 Protein Kinase, S cerevisiae↗
PubMed1980

A mathematical relationship between the fatty acid composition of the diet and that of the adipose tissue in man.

Based on literature data, the hypothesis is advanced that in human subjects a direct mathematical relationship exists between the average fatty acid composition of the habitual diet and that of the lipid stores of subcutaneous adipose tissue. Since the half-life of adipose tissue fatty acids in man is in the order of 600 days, the fatty acid pattern of depot fat provides a qualitative measure of the fat intake over a period of 2 to 3 years. It is concluded that in long-term experimental and epidemiological nutritional surveys the adipose tissue fatty acid pattern of the subjects is a useful index of the average composition of their habitual dietary fat.

Adipose Tissue↗
PubMed1983

Simultaneous financial evaluation of a complex set of capital budgeting alternatives: a mathematical model.

Capital budgeting technics provide for financial evaluation of planned purchases of equipment or other major investments. In capital budgeting, the laboratorian often is faced with a complex set of alternatives, including leasing, installment purchasing, contracting work to another laboratory, and outright purchasing. This paper presents a mathematical model useful for simultaneously evaluating the financial worth of all such alternatives under the same set of assumptions. Armed with the results of financial evaluation and evaluations of quality, turnaround time, and other patient-care factors, the laboratorian can make better decisions regarding the choice of method which, in turn, will affect the productivity of the laboratory. The model is tended for application to mutually exclusive alternatives and includes three useful capital budgeting technics: (1) payback period, (2) net present value, and (3) profitability index. The technics are demonstrated as well as a method of programming the model in financial planning software for solution by microcomputer.

Budgets↗
PubMed2004

The mathematical treatment of leaf venation: the variation in secondary vein length along the midrib.

BACKGROUND AND AIMS: In some dicotyledonous leaves and leaflets, the secondary veins run more-or-less straight to the margins and have well-defined lengths. For a given half-lamina of length L, an equation, previously proposed, relates the lengths of these veins, p, to the distances, l, between the leaf tip and their insertions on the midrib: p = B2(x+y)l(x)(L - l)(y)/L(x+y-1), where B, x and y are fitted parameters. Aspects of the formula are re-examined, including its general applicability, significance and usefulness. METHODS: Length measurements were made on leaves of various dicotyledons, notably Ulmus glabra, U. procera, Alnus viridis, A. glutinosa, Corylus avellana and Crataegus monogyna. Equations were fitted by non-linear regression. KEY RESULTS: The equation has now been applied descriptively to 23 species of eight families, but it is sometimes preferable or necessary to replace the measured length, L, with a fourth parameter that may differ significantly from it. Within a given species, values of the indices x and y are positively correlated. Leaves of some U. glabra depart qualitatively from the general pattern. As an example of hypothesis testing, the equation was used to show that the retuse or emarginate leaf tips of A. glutinosa are not due to stunting. CONCLUSIONS; That the equation applies to many species suggests that the underlying processes of leaf growth are quantitatively similar. Although relevant knowledge of these is scant, consideration of mathematical relationships may help their elucidation.

Cotyledon↗
PubMed1993

Mathematical analysis of the upper respiratory tract from an anthropometric study.

In order to design a new, performed tracheal tube adapted to the shape of the upper respiratory tract, we have undertaken an anthropometric study from lateral x-rays of the neck in 130 patients with the head in a fixed position. In order to assess different clinical situations, we studied three groups of patients: group 1 = sitting, no tracheal tube; group 2 = supine, no tracheal tube; group 3 = supine, trachea intubated. We defined a standard coordinate system and determined mathematical curves for segments of the upper respiratory tract by a polynomial regression method. With these data it was possible to study the effects of physiological variations on the shape of the curves. It was then possible to determine at which region changes occur and the factors influencing these changes. We found that the relative position of the larynx was constant, whereas the hypopharynx exhibited the greatest change with the position of the head. These observations should allow us to construct a new, performed tracheal tube with elastic compliance properties to fit the changes occurring in the region of the hypopharynx.

Adolescent↗
PubMed1996

Permissive hypercapnia and gas exchange in lungs with high Qs/Qt: a mathematical model.

Low volume ventilation with permissive hypercapnia is becoming widely used in the treatment of acute respiratory distress syndrome. A mathematical model was developed to examine the effects of hypoventilation on pulmonary gas exchange in lungs with a range of shunt fractions. Hypoventilation did not worsen gas exchange, provided the inspired oxygen concentration was high enough to maintain PAO2 at an adequate level. In lungs with a high shunt fraction, some improvement in gas exchange may result, but these effects are small. A rightwards shift of the oxygen-haemoglobin dissociation curve induced by hypercapnia, is likely to be beneficial rather than detrimental in patients with acute respiratory distress syndrome. This analysis was limited to the direct effects of hypoventilation in lungs with constant shunt fractions, and did not encompass a number of possible secondary effects such as changes in cardiac output with PaCO2, changes in shunt fraction associated with a reduction in mean airway pressure and possible direct effects of hypercapnia on the pulmonary vasculature or airways.

Adult↗
PubMed1991

A mathematical method for the comparison of three-dimensional changes in the facial surface.

Many attempts have been made to measure and compare the changes in the facial surface brought about by facial reconstructive surgery. Three-dimensional (3-D) analyses have largely consisted of qualitative descriptions rather than a quantitative treatment of these changes. Until recently, the lack of availability of 3-D data for the face and head has limited the advancement of these techniques. However, with 3-D information readily available from a laser scanning system which we have constructed, a technique has been applied which describes mathematically the facial shape and changes occurring in the face in terms of fundamental surface types. The method is described and used to compare the faces of two patients (one a cleft palate patient and the other a long-face, Class II malocclusion patient) before and after surgery along with the clinical description of the surgery, the resulting facial changes, the actual surgery performed, and the predicted surgical expectation. A strong relationship is found between the surface type description and the clinical observations. The implications of the method for surgery, facial aesthetics, and other disciplines are discussed.

Cleft Lip↗
PubMed1990

Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity.

An increased number of copies of specific genes may offer an advantage to cells when they grow in restrictive conditions such as in the presence of toxic drugs, or in a tumor. Three mathematical models of gene amplification and deamplification are proposed to describe the kinetics of unstable phenotypes of cells with amplified genes. The models differ in details but all assume probabilistic mechanisms of increase and decrease in gene copy number per cell (gene amplification/deamplification). Analysis of the models indicates that a stable distribution of numbers of copies of genes per cell, observed experimentally, exists only if the probability of deamplification exceeds the probability of amplification. The models are fitted to published data on the loss of methotrexate resistance in cultured cell lines, due to the loss of amplified dihydrofolate reductase gene. For two mouse cell lines unstably resistant to methotrexate the probabilities of amplification and deamplification of the dihydrofolate reductase gene on double minute chromosomes are estimated to be approximately 2% and 10%, respectively. These probabilities are much higher than widely presumed. The models explain the gradual disappearance of the resistant phenotype when selective pressure is withdrawn, by postulating that the rate of deamplification exceeds the rate of amplification. Thus it is not necessary to invoke a growth advantage of nonresistant cells which has been the standard explanation. For another analogous process, the loss of double minute chromosomes containing the myc oncogene from SEWA tumor cells, the growth advantage model does seem to be superior to the amplification and deamplification model. In a more theoretical section of the paper, it is demonstrated that gene amplification/deamplification can result in reduction to homozygosity, such as is observed in some tumors. Other applications are discussed.

Animals↗
PubMed1991

A mathematical model of interference for use in constructing linkage maps from tetrad data.

In determining genetic map distances it is necessary to infer crossover frequencies from the ratios of recombinant and parental progeny. To do this accurately, in intervals where multiple crossovers may occur, a mathematical model of chiasma interference must be assumed when mapping in organisms displaying such interference. In Saccharomyces cerevisiae the model most frequently used is that of R.W. Barratt. An alternative to this model is presented. This new model is implemented using a microcomputer and standard numerical methods. It is demonstrated to fit ranked tetrad data from Saccharomyces more closely than the Barratt model and thus generates more accurate estimates of map distances when used with two-point data. A computer program implementing the model has been developed for use in calculating map distances from tetrad data in Saccharomyces.

Chromosome Mapping↗
PubMed1997

A mathematical model of sialylation of N-linked oligosaccharides in the trans-Golgi network.

A mathematical model is developed of the compartmentalized sialylation of N-linked oligosaccharides in order to understand and predict the outcome of sialylation reactions. A set of assumptions are presented, including Michaelis-Menten-type dependency of reaction rate on the concentration of the glycoprotein substrate. The resulting model predicts the heterogeneous outcome of a posttranslational oligosaccharide biosynthesis step, a critical aspect that is not accounted for in the modeling of the cotranslational attachment of oligosaccharides to glycosylation sites (Shelikoff et al., Biotech. Bioeng., 50, 73-90, 1996) or general models of the secretion process (Noe and Delenick, J. Cell Sci., 92, 449-459, 1989). In the steady-state for the likely case where the concentration of substrate is much less than the Km of the sialyltransferase, the model predicts that the extent of sialylation, x, will depend upon the enzyme concentration, enzyme kinetic parameters and substrate residence time in the reaction compartment. The value of x predicted by the model using available literature data is consistent with the values of x that have been recently determined for the glycoproteins CD4 (Spellman et al., Biochemistry, 30, 2395-2406, 1991) and t-PA (Spellman et al., J. Biol. Chem., 264, 14100-14111, 1989) secreted by Chinese hamster ovary cells. For the unsaturated case, the model also predicts that x is independent of the concentration of secreted glycoprotein in the Golgi. The general modeling approach outlined in this article may be applicable to other glycosylation reactions and posttranslational modifications.

Animals↗
PubMed1994

A mathematical model for the prediction of the impact of HIV infection on tuberculosis.

A mathematical model is introduced to study the accelerating impact of HIV infection on the incidence rates of tuberculosis (TB) disease. A sexually active population (15-49 years) is followed cross-sectionally over a period of time. Beginning with the year in which HIV infection was probably first present in the population, the model calculates the growing yearly incidence rates of new TB disease in HIV-positive and in HIV-negative individuals. Model equations, derived by an actuarial method, are developed recursively. Input information required for the calculations includes the age distribution of the study population, pre-HIV annual TB infection rates, annual HIV infection and mortality rates, and estimates of annual TB disease breakdown rates in the absence and in the presence of HIV infection. With correct input data, the model provides a useful blueprint for health agencies in designing effective programmes for curbing the future course of these dual epidemics in the population.

AIDS-Related Opportunistic Infections↗