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PubMed1993

[Mathematical models applied to the growth of the ovine stomach during intrauterine life].

One hundred forty four ovine embryos and feti were used in an investigation to determine mathematical models describing the histomorphometric growth of tissues and compartments of the ruminant stomach. The results indicate that during prenatal life the diameter of the gastric chambers increase more slowly than the length. The tissue layers of the gastric walls, particularly the muscular tunic of all compartments demonstrated a uniform tendency toward more rapid development than the compartment walls proper.

Animals↗

PubMedDate not supplied

[Bifurcation analysis of a mathematical model of the interaction of cytotoxic lymphocytes with tumor cells. The effect of immunologic amplification of tumor growth and its interconnection with other "anomolous" phenomena of oncoimmunology].

Mathematical model of the immune response of the cytotoxic lymphocytes to the nonexponentially growing immunogenic tumour has been studied. Local and global biffurcations for realistic values of the parameters were determined. The connection of the oncoimmunological "anomalous" phenomena (immunostimulation of tumour growth, "sneaking through" of tumour, formation of the tumour "dormant" state) has been shown. The probability of manifestation of these effects in vivo was estimated.

Models, Biological↗

PubMed2004

[Mathematical model of dispersive infrared gas analyzer based on pyroelectric detector].

This paper analyzes the characteristics of the pyroelectric detector based on its working principle. The input andoutput mathematical model of DIGA (Dispersive Infrared Gas Analyzer) system with pyroelectric detector was established according to the design principle of DIGA. We have manufactured a novel multi-gas DIGA on the basis of this model, then pointed out several problems that should be taken into account in the design. Application indicates that this model is of considerable practical value for the design, study, performance analysis and further improvement of DIGA.

English Abstract↗

PubMed1985

Mathematical modelling of stimulus-secretion coupling in the pancreatic B-cell. IV. Dissociated time course for the glucose-induced changes in distinct Ca2+ movements.

A mathematical model for the interaction between Ca and cyclic AMP in the process of glucose-stimulated insulin release from the pancreatic B-cell is presented. This model, which takes into account such features as the stratification of cytosolic Ca and the process of Ca-stimulated Ca release from the vacuolar system, entails a dissociated time course for the effect of glucose upon distinct Ca movements. Thus, whereas glucose is postulated to cause a rapid and sustained facilitation of Ca pumping into intracellular organelles, the glucose-induced stimulation of Ca influx into the B-cell is assumed to represent a delayed and discontinuous phenomenon. Such a dissociated time course allows for a fair simulation of both 45Ca efflux and insulin release from islets perifused in the absence or presence of Ca and exposed to a sudden increase in extracellular glucose concentration.

Calcium↗

PubMed1993

Mathematical model for citric acid fermentation.

The kinetics for biomass proliferation, medium consumption and citric acid production in the course of citric acid fermentation were studied, and the mathematical models describing the course of citric acid fermentation were obtained in this paper. Based on the statistical data of experiment, the model was verified, and the model parameters were estimated with the results of the experiment. The results showed that the curves obtained by model calculation fitted with the ones determined by the experiments well, and the models described correctly the course of the citric acid fermentation. This is important for computer application to control the course of fermentation and realize the optimum of fermentation process.

Aspergillus niger↗

PubMed1995

[A mathematical model of permissible integral supercritical supersaturation of tissues by gases under decompression].

A criterion of permissible integral supercritical gas oversaturation of the body tissues was established using mathematical modelling. The heart of this criterion is that if integral supercritical oversaturation of tissues by gases does not go beyond a permissible level, gas bubbles do not reach critical volumes and give rise to decompression sickness symptoms. An equation was also built to calculate integral supercritical oversaturation of tissues during and after decompression. Permissible integral supercritical saturation values were determined for animals from mice to dogs and humans basing on literary threshold pressures with saturation and follow-on one-step decompression.

Animals↗

PubMed1996

[Silver staining of proteins separated by polyacrylamide gel electrophoresis: mathematical model].

Silver staining of proteins separated by electrophoresis in the thin layer of polyacrylamide gel can be quantitatively measured when the results are statistically treated. In the mathematical model, the reduction of protein-bound silver ions (crucial silver staining step) is considered to be autocatalytic. According to the model, the reaction rate strongly depends on the stability constant of silver complexes with functional groups of protein amino acids; and the shape of the calibration curve is determined by the ratio of concentration of silver-binding side chain groups to the reciprocal value of the stability constant. The complex shape of the curves can be explained the combination of autocatalysis and saturation. High sensitivity of this reaction to experimental conditions, contribution of complexes with different stability constants to the intensity of protein band staining, and optical effects are analyzed.

Electrophoresis, Polyacrylamide Gel↗

PubMed1997

[The enhancement of the efficacy of patient orthodontic treatment based on the mathematical modelling of prospective implant designs].

Opportunities to increase prosthetic treatment efficiency by means of applying osseointegrated implants of traditional and prospective types are analysed. A technique of mathematical modelling of the interaction between implants and jaw bone is exposed. The numerical model and applied program, developed on the basis of finite element method, enabling to analyse a stress strain state of the bone and to determine extreme safe loads on implants are described. It is shown, that the most loaded zone is a layer of the compact bone directly contiguous to the neck of the implant. That is in good agreement with the results of clinical research, according to which just this zone has the highest percentage of complications. Methods for further optimisation of implants and prosthetic structures for the purpose to perfect the techniques of prosthetic treatment are discussed.

Computer Simulation↗

PubMed1989

Mathematical modelling of metabolic pathways affected by an enzyme deficiency. Energy and redox metabolism of glucose-6-phosphate-dehydrogenase-deficient erythrocytes.

The effects of various forms of glucose-6-phosphate dehydrogenase deficiency on erythrocyte metabolism have been studied on the basis of a complex mathematical model which comprises the main pathways of this cell: glycolysis, pentose pathway, reactions of the glutathione and adenine nucleotide metabolism. The calculated flux rates through the oxidative pentose pathway with and without methylene blue are in good accord with experimental results. The degree of deficiency as predicted by the model on the basis of calculated upper oxidative load boundaries, as well as of maximal methylene blue stimulation, correlates with the individual clinical manifestation of the metabolic disease. Therefore, the model allows one to judge the degree of metabolic disorder in the presence of glucose-6-phosphate dehydrogenase enzymopathies if the kinetic properties of the defect enzyme are known. Experimentally accessible parameters for an assessment of the oxidative load capacity of cells in vivo are proposed. It is pointed out that the threshold of tolerance as to energetic load is drastically reduced in the case of severe glucose-6-phosphate dehydrogenase deficiency.

Catalysis↗

PubMed2006

A nonlinear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt.

We present a development of a model [Tomlinson, I.P.M., Bodmer, W.F., 1995. Failure of programmed cell death and differentiation as causes of tumors: Some simple mathematical models. Proc. Natl. Acad. Sci. USA 92, 11130-11134.] of the relationship between cells in three compartments of the intestinal crypt: stem cells, semi-differentiated cells and fully differentiated cells. Stem and semi-differentiated cells may divide to self-renew, undergo programmed death or progress to semi-differentiated and fully differentiated cells, respectively. The probabilities of each of these events provide the most important parameters of the model. Fully differentiated cells do not divide, but a proportion undergoes programmed death in each generation. Our previous models showed that failure of programmed death--for example, in tumorigenesis--could lead either to exponential growth in cell numbers or to growth to some plateau. Our new models incorporate plausible fluctuation in the parameters of the model and introduce nonlinearity by assuming that the parameters depend on the numbers of cells in each state of differentiation. We present detailed analysis of the equilibrium conditions for various forms of these models and, where appropriate, simulate the changes in cell numbers. We find that the model is characterized by bifurcation between increase in cell numbers to stable equilibrium or explosive exponential growth; in a restricted number of cases, there may be multiple stable equilibria. Fluctuation in cell numbers undergoing programmed death, for example caused by tissue damage, generally makes exponential growth more likely, as long as the size of the fluctuation exceeds a certain critical value for a sufficiently long period of time. In most cases, once exponential growth has started, this process is irreversible. In some circumstances, exponential growth is preceded by a long plateau phase, of variable duration, mimicking equilibrium: thus apparently self-limiting lesions may not be so in practice and the duration of growth of a tumor may be impossible to predict on the basis of its size.

Animals↗

PubMedDate not supplied

[Vector mathematical model for the analysis of complex movements in 3-dimensional space exemplified by the divided symphysis].

For the analysis of complex movements in the divided pubic symphysis of cadavers a vector-mathematical model was developed. Overall movements is analysed in components, as translations in the three dimensions of space and rotations around the three axes of space, as error-free and as simply as possible by measuring the distances to different defined points. Experimental conditions, the development of a vector-mathematical system of analysis, error analysis and interpretation of results are shown. With this method it also possible to analyse similar problems in the same way.

Biomechanical Phenomena↗

PubMed1992

Role of the myogenic mechanism in the genesis of microvascular oscillations (vasomotion): analysis with a mathematical model.

The possibility that spontaneous oscillations in microvessel caliber, called vasomotion, arise from the activity of the local myogenic mechanism is analyzed in this work using an original mathematical model. According to experimental results, the model assumes that the myogenic response in microcirculation (transverse arterioles and terminal precapillary-postcapillary microvessels) is characterized by both a static and a dynamic (i.e., rate-dependent) component. Computer simulations demonstrate that the myogenic mechanism of action, thanks to its strong rate-dependent component in terminal arterioles, can produce vascular instability and oscillations of vessel caliber without the need to assume the existence of a local pacemaker in smooth muscle cells. Moreover, these oscillations turn out similar, both in frequency and in shape, to those experimentally observed in microvascular networks. Finally, according to experimental data, several kinds of vasodilatory stimuli (such as arterial hypotension, increase in the tissue metabolic rate, and postischemic reactive hyperemia) cause stoppage of vasomotion and stabilization of vessel caliber.

Animals↗

PubMed1977

Role of Concentration-dependent Unloading in Mathematical Models of Münch Transport.

It has been erroneously claimed (Goeschl et al. [1976] Plant Physiol. 58: 556-562) that concentration-dependent unloading is required for a correct mathematical solution for Münch phloem transport. Although it may prove to be physiologically correct, concentration-dependent unloading is not a mathematical necessity. Furthermore, its use in a mathematical model may not be desirable, because there is an infinite family of solutions for any given unloading distribution, irrespective of whether concentration-dependent unloading is assumed. Some illustrative numerical results are presented.

Journal Article↗

PubMed1991

Insights into hazard from intense impulses from a mathematical model of the ear.

In order to provide insight into the mechanisms that operate in the ear when it is exposed to intense sounds, time and frequency domain mathematical models of the ear including significant nonlinearities in the middle ear were developed to trace energy flow from the free field to the inner ear and ultimately allow the calculation of basilar membrane displacement and a consequent hazard function. These models match the ear's behavior at low intensities and also reproduce many of the features of the data on hearing hazard from intense impulses. They provide critical insights into the loss mechanisms, suggest new strategies for protecting hearing as well as reducing hazard at the source and could also serve as a framework for a new, accurate, theoretically based method for rating hazard from intense sounds.

Animals↗

PubMed1977

Trichloroethylene exposure. Simulation of uptake, excretion, and metabolism using a mathematical model.

The absorption, distribution, and excretion of trichloroethylene, as well as the kinetics of formation and elimination of trichloroethanol (TCE) and trichloroacetic acid (TCA) were simulated by a mathematical model. The results of this model have been satisfactorily compared with those obtained experimentally from pulmonary elimination of the solvent and from urinary excretion of the metabolites. The model permitted a study of the distribution of the solvent in the different tissues of the organism as well as an evaluation of the body burden of TCE and TCA. The influence of the duration and repetition of the exposure on the urinary eliminations of TCE and TCA was studied, and showed that the excretion of the first metabolite represents the most recent exposure while that of the second is related to the average exposure of the preceding days. The study of the pulmonary elimination of trichloroethylene during single or repeated exposures showed a linear relationship between the alveolar concentration of the solvent approximately 15 hours after the end of the exposure and the quantity of trichloroethylene accumulated in the fatty tissues.

Environmental Exposure↗

PubMed2004

Large liver tumors: protocol for radiofrequency ablation and its clinical application in 110 patients--mathematic model, overlapping mode, and electrode placement process.

PURPOSE: To establish a preoperative protocol for ultrasonographically guided percutaneous radiofrequency (RF) ablation of large liver tumors that is based on mathematic models and clinical experience and to evaluate the role of this protocol in RF ablation. MATERIALS AND METHODS: A regular prism and a regular polyhedron model were used to develop a preoperative protocol for liver tumor ablation. This protocol enabled the authors to minimize the number of ablation spheres, optimize the overlapping mode, and determine the electrode placement process. One hundred ten patients with 121 liver tumors were treated by using this protocol. Sixty-nine patients had 74 hepatocellular carcinomas (HCCs), and 41 had 47 metastases to the liver (ie, metastatic liver carcinomas [MLCs]). Patients underwent follow-up helical computed tomography (CT) 1 month and every 2-3 months after RF ablation. Ablation was considered a success if no contrast enhancement was detected in the treated area on the CT scan obtained at 1 month. RESULTS: A total of 536 ablations were performed in the 121 tumors. The ablation success rate was 87.6% (106 of 121 tumors); the local recurrence rate, 24.0% (29 of 121 tumors); and the estimated mean recurrence-free survival, 17.1 months. Twenty-five patients underwent 38 re-treatments for local tumor recurrence. Major complications occurred in seven patients. Of these patients, only one, who had a tumor close to the colon, had a colon perforation 1 week after RF and required surgical intervention. CONCLUSION: The described protocol for treatment of large tumors had a success rate of 87.6% and a local recurrence rate of 24.0%.

Adult↗

PubMed2005

A mathematical model of peritoneal fluid absorption in tissue.

To investigate how water flow and interstitial pressure change in tissue during a peritoneal dwell with isotonic fluid, we developed a mathematical model of water transport in the tissue. Transport through muscle alone (M) and through muscle with intact skin (MS) were considered for the rat abdominal wall, using various parameters for muscle and skin. Based on the concept of distributed capillary and lymphatic systems, two main transport barriers were taken into account. capillary membrane and interstitium. We calculated the tissue hydrostatic pressure profiles and compared them with experimental data. The theoretic steady-state pressure distribution for model M is in good agreement with the experimental data. In model MS, the theoretic distribution diverges from the data in the subcutaneous layer. The transient times for fluid flow in the tissue for both model simulations are rather long (40 minutes in model M and 95 minutes in model MS) and depend on intraperitoneal pressure. The fraction of fluid absorbed from the tissue by the lymphatics increases with time from 10% to 97% of fluid flow from the peritoneal cavity.

Abdominal Muscles↗

PubMedDate not supplied

[Mathematical model of two pathways of light perception by the photoreceptor cell].

On the basis of the concept postulating polyfunctional role of rhodopsin in the photoreceptor cell excitation a mathematical model of two pathways of excitation was formulated. One pathway involves the appearance of Ca2+ ions in the cell, which block the sodium channels. The second one results in cGMP splitting which also brings about the blocking of sodium channels. A change in the concentration of acting agents and development of cell excitation under illumination was calculated. The calcium branch is shown to be rapid and direct, but of a low sensitivity. The cGMP branch is a slow one but has a high intensification coefficient. The action time of the calcium branch does not depend on illumination, while the time of cGMP branch decreases with the illumination rise and is in an inverse proportion to the square root of the flash intensity. Under repeated illumination the amplitude of calcium response decreases, and its time remains constant. In cGMP branch the time of the response to the second flash decreases. The amplitude of the second response depends on the intensity of the first flash, it can be smaller or larger than the amplitude of the first response.

Cyclic GMP↗