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At least 1,585 records · Page 88Linked to original sources
PubMed2005

Near-real-time radiotherapy dosimetry using optically stimulated luminescence of Al2O3:C: mathematical models and preliminary results.

In this paper we report investigations aimed toward applying optically stimulated luminescence (OSL) of Al2O3:C for near-real-time medical dosimetry, especially in radiotherapy. The classical mathematical model normally used for the description of OSL phenomena was expanded to predict the behavior of the luminescence signal in the case when the OSL sample is simultaneously irradiated and optically stimulated. The predictions obtained were used to develop different measurement approaches and correction algorithms for the luminescence signals, thus enabling dose estimation from OSL during rather then after the irradiation procedure. Radiation probes with diameters of less than 1 mm, suitable for the envisioned in-vivo measurements were constructed by attaching small Al2O3:C crystals to optical fiber cables. The OSL fiber probes and a purpose-built, portable OSL stimulation and readout system were used to measure doses at speeds up to 1 data point every 3s, under irradiation at dose rates of the same order of magnitude as those found in conventional radiotherapy techniques. The corrected OSL signal was found to be proportional to the absorbed dose, and accurately followed sudden transitions in the irradiation dose rate.

Algorithms↗
PubMed1982

Penetration of antibiotics into vegetation of heart valves: a mathematical model.

The effect of vegetation size upon the concentration of antibiotic within various points of a fibrin-clot heart valve vegetation such as ones found in bacterial endocarditis was examined. A mathematical model based upon Fick's second law of diffusion was developed and solved on a PDP-II computer. The antibiotic was assumed to have a half-life of 30 min and intermittently injected intravenously every 4 h. After 5 simulated antibiotic doses, peak and trough levels of the antibiotic near the center of the vegetations of sizes 0.5, 1.0, 2.0 cm were, respectively, 37 and 3%, 22 and 15%, and 18 and 18% of the free serum antibiotic concentration. This model can be used to estimate antibiotic levels in different areas of a valvular vegetation.

Absorption↗
PubMed2003

[Research on human eye cornea's mathematical model and application in diopter correction].

The excimer laser diopter correction has proven to be efficient and safe. This paper presents the principle of excimer laser refractive surgery. Based on analyzing the mathematics model of the human eye cornea, the authors have proposed a new model which can be used to proceed the myopia, hyperopia, astigmatism diopter correction. Also studied were the excimer laser's ablation mechanism and the flying-spot scanning technology. The research results have been directly applied to Ophthalmic excimer laser system. The correction of diopter is well improved.

Algorithms↗
PubMed1980

Mathematical model of mean age, mean arsenic dietary dose and age-specific prevalence rate from endemic chronic arsenic poisoning: a human toxicology study.

The aim of this investigation was to develop a mathematical model of mean age, mean arsenic dietary dose, and age-specific prevalence rate for endemic chronic arsenic poisoning. Data on mean age (years), mean arsenic dietary dose (mg/kg body weight/day), and age-specific prevalence rate per 100,000 population for endemic chronic arsenic poisoning in Antofagasta Commune, northern Chile, for the 1968-1971 period, were collected. Endemic chronic arsenic poisoning means here chronic arsenical dermatosis associated with marked or sever symptoms (or signs) of chronic arsenic poisoning (chronic diarrhoea, hepatic cirrohsis, chronic bronchitis, bronchiectasis, recurrent broncho-pneumonia, cardiomegaly, systemic occlusive arterial disease, cerebral thrombosis, etc.) There was a strong positive correlation between age-specific prevalence rate per 100,000 population and mean arsenic dose (r = + 0.9593) and a negative correlation between prevalence rate and mean age (r = 0.8789). These findings show that the prevalence rate declines with the advancing age and increases with the increase of arsenic dose. A multiple linear regression model E(y) = alpha + beta X1 + gamma X2, where y represents the age-specific prevalence rate per 100,000 population, X1 the mean arsenic dose, and X2 the mean age, was fitted to the data. The estimates of the parameters (alpha, beta, and gamma) were obtained by minimizing the residual sum of squares sigma(y - alpha - beta X1 - gamma X2)2. The following multiple linear regression equation was obtained: Y = 202.161 + 8452.455 X1 - 2.394 X2. Of the total variability in the prevalence rate, 96.22 per cent was accounted for by the multiple regression.

Adolescent↗
PubMed1997

[Mathematical model application in the design of methods for reconstructive surgery of the stomach].

Advantages and faults of reconstructive operations after stomach resection according to Billroth-II were analyzed using principles of mathematical modelling on entire electroconductive mediums. Optimal method of the longitudinal axis of small intestine placement under an acute angle to the lesser curvature of stomach promotes the pressure reduction in the region of stomach and intestine junction prevents the hydrodynamic shock appearance, provides a smooth transference of the stomach contents while its emptying.

Humans↗
PubMed2002

A mathematical model of pattern formation in the vascular cambium of trees.

The beautiful patterns apparent in wood grain have their origin in the alignment of fusiform initial cells in the vascular cambium of trees. We develop a mathematical model to describe the orientation of fusiform initial cells, and their interaction with the plant hormone indole-3-acetic acid (auxin). The model incorporates the following four assumptions: (1) auxin is actively transported parallel to the long axis of the initials, (2) auxin diffuses perpendicular to the long axis of the initials, (3) the initials tend to orient parallel to the flux of auxin through the cambium, and (4) adjacent initials tend to orient parallel to one another. Each assumption is justified on the basis of available evidence and cast in mathematical form. Our main result is a pair of nonlinear differential equations that describe the coupling between the distribution of auxin in the cambium and the orientation of fusiform initials. Numerical solutions to the equations show qualitative resemblance to the wood grain patterns observed at branch junctions, wounds and knots, and topological defects.

Diffusion↗
PubMed2001

Mathematical models of eye movements in reading: a possible role for autonomous saccades.

An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory - almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes.

Algorithms↗
PubMed2000

Red blood cell osmotic fragility confidence intervals: a definition by application of a mathematical model.

The red blood cell osmotic fragility test is based on the measure of the resistance of red blood cells to lysis as a function of decreasing NaCl concentration. Up to now, several methods have been used for recording these data, but for the first time, the human red blood cell osmotic fragility confidence interval using the Orcutt mathematical model was determined. The absorbance of the hemoglobin measured at 540 nm, released by the red blood cells of 40 healthy adult individuals, was fitted to the equation Absorbance=p3 erfc ([NaCl] - p1/p2); p3 measures one half the absorbance produced by maximum red blood cell hemolysis, p1 is the [NaCl] producing 50% red blood cell hemolysis, and p2 is the dispersion in [NaCl] producing red blood cell hemolysis. Confidence intervals (mean+/-SD) for the three parameters were as follows: p1=4.2718+/-0.1848; p2=0.1947+/-0.0391, and p3=0.5568+0.0426. The usefulness of this osmotic fragility data analysis method using two pathological samples (beta-thalassemia minor and hereditary spherocytosis) was demonstrated. Parameters of the fitted data were compared with those obtained by the conventional recording method of Beutler.

Adult↗
PubMed2003

Flavor release measurement by atmospheric pressure chemical ionization ion trap mass spectrometry, construction of interface and mathematical modeling of release profiles.

An instrumental on-line retronasal flavor analysis was developed to obtain information about the release of flavor compounds in expired air from humans during eating. The volatile flavor compounds were measured by ion trap mass spectrometry with an atmospheric pressure chemical ionization source (APCI). An interface was designed to sample the breath directly from the nose. The repeatability in vitro for seven different flavor compounds came out with relative standard derivation less than 10% in most cases, which is acceptable. In vitro quantification was carried out by a determination of the concentration in the gas phase over a flavor solution by GC/MS, followed by measurements of intensities by the APCI ion trap. Ion suppression by acetone in the breath was negligible at concentration levels relevant in these experiments. The instrumental limits of detection for menthone and menthol coincide with that of the flavor detection threshold. An application study on the release of menthone and menthol from chewing gum by a group of six test persons was performed. Flavored chewing gum was used as a model matrix because of the long chewing periods and the simplicity of the system. It is concluded that the interface and the method can be used to measure breath from the nose. A mathematical model of the data was developed to give a quantitative method for description and characterization of the release of flavor compounds. The release profiles consisted of two sequences, one for a chewing period, and one for a phasing out process. The proposed method for modeling provided a reasonable description of the release process. In addition to flavor compounds, this new interface and mathematical application could provide information on chemicals in the human breath, which could be interesting, for example, within medical diagnosis.

Journal Article↗
PubMed1980

Dynamics of the biological response to molecular injury: a mathematical model.

This paper introduces a mathematical interpretation of the behaviour of a cell population (bacterial or eucaryotic) exposed to a genetically harmful agent (chemical or physical) administered with a given time-dependent intensity. The model described here provides a simple representation of the kinetics of the following processes; (i) induction of the cell damage; (ii) repair of the molecular injury; (iii) cell proliferation; (iv) cell death. The model has been shown to be consistent with two independent sets of experimental data concerning the tumour growth after irradiation. These data were drawn from the literature, and their numerical fitting has been achieved successfully.

Cell Division↗
PubMed1979

Mitotic index, influx and mean transit time in the hamster cheek pouch epithelium, a partially synchronized cell system. Presentation of a mathematical model based on a non-stationary probability density function for the transit time in a compartment.

Mitotic activity was followed in the epithelium of the hamster cheek pouch for about 12 hr in two experiments under different conditions of noise and light intensity. A mathematical model based on a non-stationary probability density function for the transit time through mitosis was developed, making an analysis of this partially synchronized cell system possible. The most important result of the two experiments is the indication of a non-stationary mean transit time for cells in mitosis. In the first experiment (70 dB, 103 lux), which produced high mitotic indices (maximum 2.0%), the influx changed from 0. to 0.9%/hr (mean of 7-hourly determinations: 0.4%/hr), and the mean transit time from 1.9 to 5.5 hr. In the second experiment (70 dB, 265 lux), which had a lower level of MI (maximum 1.3%), the influx changed from 0 to 1.8%/hr (mean of 13-hourly determinations: 0.4%/hr), and the mean transit time from 0.3 to 3.3 hr. It was difficult to say precisely whether the variation in influx or in mean transit time was the main factor in the increase and decrease of MI. The data could not be simulated with a stationary mean transit time. It is suggested that changes in MI due to different external circumstances are mainly the result of variation in the mean transit time.

Animals↗
PubMed1997

A mathematical model of the intracranial system including autoregulation.

Cerebral autoregulation plays an important role in the dynamic processes of intracranial physiology. This work develops a four-compartment, lumped-parameter model for the interactions of intracranial pressures, volumes, and flows as a test bed for examining the consistent inclusion of explicit autoregulation in mathematical models of the intracranial system. It is hypothesized that autoregulation of the blood supply from the arterioles to the capillary bed can be modeled by allowing the flow resistance at the interface of the artery and capillary compartments in the model to be a function of pressure rather than a constant. The functional dependence on pressure of this resistance parameter is not specified in advance, but emerges naturally from the assumed relationship between pressure differences and flows. Results show that a constant flow from the artery to the capillary compartment can be maintained by a flow resistance which is resistance which is directly proportional to the pressure difference between these two compartments. Oscillatory flow is reestablished in the model at the capillary-cerebrospinal fluid and capillary-venous interfaces.

Animals↗
PubMed2003

Weibull distribution function based on an empirical mathematical model for inactivation of Escherichia coli by pulsed electric fields.

The pulsed electric field inactivation kinetics of Escherichia coli suspended in orange juices with three different concentrations of carrot juice (0, 20, and 60%) was studied. Electric field strengths ranged from 25 to 40 kV/cm, and treatment times ranged from 40 to 340 micros. Experimental data were fitted to Bigelow, Hülsheger, and Weibull distribution functions, and the Weibull function provided the best fit (with the lowest mean square error). The dependency of each model's kinetic constant on electric field strength and carrot juice concentration was studied. A secondary model was developed to describe the relationship of Weibull parameters a and n to electric field strength and carrot juice concentration. An empirical mathematical model based on the Weibull distribution function, relating the natural logarithm of the survival fraction to treatment time, electric field strength, and carrot juice concentration, was developed. Parameters were estimated by a nonlinear regression. The results of this study indicate that the error rate for the model's predictions was 6.5% and that the model was suitable for describing E. coli inactivation.

Beverages↗
PubMed1996

Ion currents underlying sinoatrial node pacemaker activity: a new single cell mathematical model.

The ionic currents underlying autorhythmicity of the mammalian sinoatrial node and their wider contribution to each phase of the action potential have been investigated in this study using a new single cell mathematical model. The new model provides a review and update of existing formulations of sinoatrial node membrane currents, derived from a wide range of electrophysiological data available in the literature. Simulations of spontaneous activity suggest that the dominant mechanism underlying pacemaker depolarisation is the inward background Na+ current, ib,Na. In contrast to previous models, the decay of the delayed rectifying K+ current, iK, was insignificant during this phase. Despite the presence of a pseudo-outward background current throughout the pacemaker range of potentials (Na-K pump+leak currents), the hyperpolarisation-activated current i(f) was not essential to pacemaker activity. A closer inspection of the current-voltage characteristics of the model revealed that the "instantaneous" time-independent current was inward for holding potentials in the pacemaker range, which rapidly became outward within 2 ms due to the inactivation of the L-type Ca2+ current, iCa,L. This suggests that reports in the literature in which the net background current is outward throughout the pacemaker range of potentials may be exaggerated. The magnitudes of the action potential overshoot and the maximum diastolic potential were determined largely by the reversal potentials of iCa,L and iK respectively. The action potential was sustained by the incomplete deactivation of iCa,L and the Na-Ca exchanger, iNaCa. Despite the incorporation of "square-root" activation by [K]o of all K+ currents, the model was unable to correctly simulate the response to elevated [K]o.

Action Potentials↗
PubMed2003

Mathematical model of renal elimination of fluid and small ions during hyper- and hypovolemic conditions.

This study is concerned with the formulation of a 'kidney module' linked to the plasma compartment of a larger mathematical model previously developed. Combined, these models can be used to predict, amongst other things, fluid and small ion excretion rates by the kidney; information that should prove useful in evaluating values and trends related to whole-body fluid balance for different clinical conditions to establish fluid administration protocols and for educational purposes. The renal module assumes first-order, negative-feedback responses of the kidney to changes in plasma volume and/or plasma sodium content from their normal physiological set points. Direct hormonal influences are not explicitly formulated in this empiric model. The model also considers that the renal excretion rates of small ions other than sodium are proportional to the excretion rate of sodium. As part of the model development two aspects are emphasized (1): the estimation of parameters related to the renal elimination of fluid and small ions, and (2) model validation via comparisons between the model predictions and selected experimental data. For validation, model predictions of the renal dynamics are compared with new experimental data for two cases: plasma overload resulting from external fluid infusion (e.g. infusions of iso-osmolar solutions and/or hypertonic/hyperoncotic saline solutions), and untreated hypo volemic conditions that result from the external loss of blood. The present study demonstrates that the empiric kidney module presented above can provide good short-term predictions with respect to all renal outputs considered here. Physiological implications of the model are also presented.

Algorithms↗
PubMed2003

Unloading effect of a rotary blood pump assessed by mathematical modeling.

Due to the increased appeal of rotary blood pumps for long-term cardiac assist, we conducted a study of their capacity to unload the left ventricle (LV). We used a validated mathematical model of the cardiovascular system and implemented the pump characteristics of an investigational microdiagonal pump (Medos). The influence of the pump on systemic hemodynamics, LV energetic parameters, and wall stress was evaluated in continuous and synchronous pulsatile modes of operation. For the continuous mode simulations, the influence of heart rate, LV contractility, and pump speed was assessed in a parametric study. For the pulsatile mode, different onsets of a synchronous time-varying pump speed pattern were tested. Our data indicate that the effectiveness of unloading in continuous mode depends on the contractility of the native ventricle. Hypocontractile ventricles are most easily unloaded, while ventricles with moderate contractility require high continuous pump speeds to achieve notable unloading. In pulsatile mode, the pump timing is an important determinant of pump/cardiovascular system interaction, with a counterpulsation setting yielding the best unloading.

Biomechanical Phenomena↗
PubMedDate not supplied

Mathematical modeling of the first inflation of degassed lungs.

The pressure-volume (P-V) relationship of degassed lungs during the first inflation is different from that in consecutive inflations. We developed a mathematical model of the P-V curve of the first inflation by assuming that (1) central airways are open leading to many subtrees of n generations that are initially closed; (2) an airway opens when inflation pressure reaches the opening threshold pressure of that segment; and (3) the opening threshold pressures do not depend on airway generation. In this model, airway opening occurs in cascades or avalanches. To test the model which contains only two parameters, n and a pressure, P(low), at which at least one subtree completely opens, we measured the first inflation P-V curves of 15 excised and degassed rabbit lungs. By fitting these data, we found that n=17+/-5, P(low)=23+/-4 cmH2O, and that there is a wide distribution of threshold pressures for airways with diameters <2 mm. Analysis of the P-V curve in a lung which was lavaged with a liquid of constant surface tension and in which airways are presumably open demonstrated that the distribution of threshold pressures is narrow, and hence no avalanches occur during inflation. We conclude that in normal lungs the first inflation is dominated by avalanche behavior of airway opening providing information on the global distribution of threshold pressures and the average site of airway closure.

Animals↗
PubMed2003

Bacterial resistance to penicillin G by decreased affinity of penicillin-binding proteins: a mathematical model.

Streptococcus pneumoniae and Neisseria meningitidis have very similar mechanisms of resistance to penicillin G. Although penicillin resistance is now common in S. pneumoniae, it is still rare in N. meningitidis. Using a mathematical model, we studied determinants of this difference and attempted to anticipate trends in meningococcal resistance to penicillin G. The model predicted that pneumococcal resistance in a population similar to that of France might emerge after 20 years of widespread use of beta-lactam antibiotics; this period may vary from 10 to 30 years. The distribution of resistance levels became bimodal with time, a pattern that has been observed worldwide. The model suggests that simple differences in the natural history of colonization, interhuman contact, and exposure to beta-lactam antibiotics explain major differences in the epidemiology of resistance of S. pneumoniae and N. meningitidis.

Bacterial Proteins↗