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At least 37 records · Page 2Linked to original sources
PubMed2006

Optimal size and location for corneal rotational autografts: a simplified mathematical model.

OBJECTIVE: To calculate clinical guidelines for the optimal location and size of a rotational autokeratoplasty. METHODS: The ideal graft size and trephine decentration for a rotational autograft were calculated based on scar location using geometric models. Mathematical variables were set to maximize postoperative visual acuity and for generalization of the geometric model. This model was used in a rotational autokeratoplasty of a patient with a history of a corneal scar and diplopia. An 8-mm autograft was decentered 0.5 mm superiorly and rotated 180 degrees to relocate the scar to the superior aspect of the cornea, out of the patient's vision. RESULTS: For cases that satisfy the given variables, a graft diameter of 8 mm with a decentration of 0.5 mm balances maximization of scar removal and scar movement superiorly, with minimization of discrepancy in corneal thickness after rotation. For scars that are alpha degrees from horizontal, the graft should be rotated 180 - alpha degrees . By using these calculations, the autograft in this case successfully resolved the diplopia and improved visual acuity. CONCLUSIONS: A rotational autograft can be an effective alternative to standard penetrating keratoplasty for some patients with corneal scars. We establish a mathematical model for most clinical instances of a rotational autograft, in which an 8-mm graft with a decentration of 0.5 mm best satisfies the goals of surgery.

Adult↗
PubMed1984

Selective effects of secretagogues on insulin secretion: a mathematical model.

A mathematical model of the secretion of insulin from pancreatic islets of Langerhans is proposed. Previously proposed mathematical models of insulin secretion have dealt solely with glucose-stimulated release, and not with the more complex patterns of secretion (such as "off-responses") in response to other secretagogues or combinations of secretagogues. We conclude that an off-response is consistent with a compartmental model; and the facilitating effect of a constant concentration of glucose on leucine-stimulated insulin secretion is consistent with a selective effect of glucose on a single compartment of the model.

Animals↗
PubMed2004

Administration of Zn-Co-Mn basic salt to chickens with ascaridiosis. I. A mathematical model for Ascaridia galli populations and host growth with and without treatment.

A newly synthesized basic mixed salt (Zn(x)Co(y)Mn(1-x-y)) x (OH)6SO4 x 2H2O) was administered to chickens with ascaridiosis. Improvement in survival, gain in body weight (of 19.03%) and restoration of microelement content were observed in the treated chickens. An increase in the gain in body weight of 7.62% in uninfected treated chickens was also observed. The establishment of Ascaridia galli populations in chickens, and chicken growth in control and infected hosts, untreated and treated, were modelled mathematically. Some kinetic parameters (the rate of reduction of the nematode population nu and the relative rate mu of gain in body weight of the host) were determined. The values of nu =0.027 day(-1) and nu* =0.032 day(-1) were calculated for the reduction rates in infected, untreated chickens and in infected, treated chickens, respectively. The worm burden in infected, treated chickens was 20.4% lower than in infected, untreated chickens.

Animals↗
PubMed2000

Mathematical modeling of chronical hypoxia in tumors considering potential doubling time and hypoxic cell lifetime.

PURPOSE: To model mathematically how potential doubling time and hypoxic cell lifetime affect the extent of chronical hypoxia in tumor tissue segments. Three capillary geometries were modeled under idealized steady state conditions. MATERIALS AND METHODS: The capillary geometries are: tissue surrounding an axial capillary, tissue enclosed by a cylindrical capillary network, and tissue enclosed by a spherical capillary network. The tissue segments are modeled as three-compartment systems, where well nourished cells proliferate near the vasculature and, in so doing, displace 'older' cells into a quiescent compartment and, ultimately into a hypoxic region. The extent of the hypoxic zone is the distance traversed by cells during their hypoxic lifetime before becoming necrotic. The steady state situation, where the necrotic cell loss equals the cell gain caused by cell proliferation was investigated. RESULTS: The hypoxic fraction, HF, was found to be inversely proportional to the potential doubling time of the tumor segment, T(pot), and proportional to the hypoxic cell lifetime, T(hypox). The extent of the oxygenated zone depends only on the capillary geometry, the capillary radius, the intracapillary oxygen tension, and the tissue respiration rate. The extent of the hypoxic zone in addition depends on T(pot) and T(hypox). CONCLUSIONS: Mathematical modeling of idealized steady state conditions shows that the ratio of hypoxic cell lifetime and potential doubling time, T(hypox)/T(pot), determines the hypoxic fraction, HF, in tumor segments. The extents of the oxygenated and the hypoxic zones can be predicted from the models.

Capillaries↗
PubMed1989

Physical properties of resistance vessel wall in peripheral blood flow regulation--I. Mathematical model.

A mathematical model is introduced to investigate the influence of the physical properties of the resistance vessel wall on the metabolic and myogenic mechanisms. The resistance vessel wall is assumed to have an elastic property and the elastic modulus to be a function of pressure (myogenic) and flow (metabolic). Blood is Poiseuille's flow. The resulting mathematical equations for pressure-flow, pressure-diameter, pressure-wall tension and pressure-wall elastic modulus relationships introduced obey Laplace's law. Poiseuille's law and Hooke's law. In comparison with the experimental data (pressure diameter), the mathematical model is confirmed to explain well the dynamic behavior of the resistance vessel wall in vivo.

Elasticity↗
PubMedDate not supplied

[Interactive determination of the parameters of mathematical models in planning radiotherapy of malignant tumors. 3. Method of local adjustment of the parameters of mathematical models (examples of application)].

To increase the accuracy of calculation of tolerance doses of the likelihood of radiation-induced complications in normal organs and tissues by using mathematical models, the author has developed a method for local mathematical model parameter adjustment (LMMPA) which included analysis of the structure of a mathematical model, systematization of clinical information and its goal-oriented use to determine the parameters of a model. The necessity of developing the LMMPA method stemmed from the complexity of the body exposed to radiation a system and from the quest for taking into account the impact of the system on the values of mathematical models. LMMPA may be regarded as the extension of determination of the parameters of mathematical models or as the interactive determination of their parameters that describing radiation exposures of complex biological systems. Different aspects of using of LMMPA are indicated how to apply it to the determination of tolerance doses for connective tissue, lung tissue, and the brain by using the Ellis and LQ models. The extended LMMPA is shown how to determine the parameters of a mathematical models for calculation of the likelihood of radiation-induced complications in the lung tissue.

Brain↗
PubMed1987

Epidermal cell proliferation. II. A comprehensive mathematical model of cell proliferation and migration in the basal layer predicts some unusual properties of epidermal stem cells.

The clustering of 3HTdR labelled cells in the epidermal basal layer and their changes with time have been modelled mathematically and cannot be adequately fitted by an earlier model of the cell kinetic organisation of the skin. A more refined model analysis was performed based on Monte Carlo computer simulations of cell layers which take cell division, cell aging and lateral as well as vertical cell migration into account. A large variety of hypothetical scenarios was tested to see if each could provide a fit to the clustering data. The analysis provides further support for the concept of a cell kinetic heterogeneity with a stem-transit-postmitotic differentiation scheme. In the best overall model scheme three transit divisions are predicted but unlike in the earlier model it is now postulated that postmitotic cells can be produced at all stages in the lineage rather than only at the end of the amplification scheme. Most important, the model predicts that stem cells and most of the transit cells differ in the way they process 3HTdR label. Grain dilution is an important mechanism to explain the fate of some labelled cells in the tissue, but on its own it can only consistently explain the data if the stem cells have a very low labelling index (LI less than or equal to 1%) which implies a very short biologically unreasonable S-phase. If a higher LI (longer S-phase) is assumed for the stem-cells other mechanisms must be predicted to explain the lack of large clusters and the increase in time of the singles. The selective segregation of chromosomes at mitosis is one such mechanism. However, on its own a large number of cells would have to behave in this way (i.e. both stem and T1 cells). If combined with other assumptions such as some grain dilution this selective segregation may be restricted only to stem cells. In addition the model allows cell production and migration rates to be estimated and the analysis can be related to the EPU-concept. Indeed the model itself would tend to automatically generate an EPU like structure. The model quantitatively reproduces LI, PLM, CL and clustering data.

Autoradiography↗
PubMed1992

Mathematical modelling of the elastic properties of retina: a determination of Young's modulus.

The retina can be regarded as an elastic membrane or sheet which stretches and deforms when a force is applied to it. Isolated bovine retina was taken and a graded traction force applied to determine retinal profile as a function of force. The resulting profile can be modelled mathematically and the model then used to determine a value for the elastic constant. The value of the elastic constant obtained by this method is approximately 2 N/m. This value of the elastic constant, combined with the observed retinal thickness, yields a value of Young's modulus for retina of approximately 2 x 10(4) Pa, which is about 2 orders of magnitude weaker than typical rubber. This value can then be used in modelling retinal behaviour in vivo when forces are applied to detached retina.

Animals↗
PubMedDate not supplied

[Assessment of the potential impact in Italy of extensive varicella vaccination programs based on a mathematical model].

A mathematical model has been developed in order to assess the effect of extended programs of varicella vaccination on the epidemiology of the disease in Italy. The effect of different vaccination options have been estimated by the change in incidence of the disease and age distribution of cases over a short and long period of time. The developed mathematical model reproduces chickenpox transmission and immunisation; five strategies different for target age of vaccination and/or proportion of vaccinated subjects have been considered. In all scenarios the model pointed out an initial decrease of case frequency observed in the first 3-5 years, followed by a series of epidemic peaks, variable in number and size by vaccination strategy. Moreover, as the number of cases among infants decreases, the number of cases among adults increases. Such event is minimised only by very high vaccination coverage (80% in the first year of life and 50% at 12 years of age). Extensive programmes of vaccination against chickenpox must reach a high coverage as soon as possible in order to avoid undesirable effects that may move forward the age of cases and therefore should be offered to target age groups easy to reach.

Chickenpox↗
PubMedDate not supplied

[Mathematical models of dose fractionation based on LQ function. (population-tissue models)].

A mathematical model was developed to calculate the probability of tumor tissue sterilization. It is assumed that tumor tissue contains normal and radio-resistant tumor cells and the survival of both types of tumor cells can be described by LQ functions. A package of programmes was created to solve the extreme problems in the determination of the parameters of LQ functions and the relative count of radio-resistant cells in the volume of tumor tissue. A programme complex was devised to solve practical tasks in radiological care. The series of tasks, which illustrate various aspects of determination of the parameters of the mathematical model by using clinical data and calculating the probability of tumor tissue radiation sterilization.

Carcinoma, Squamous Cell↗
PubMedDate not supplied

[The interactive determination of the mathematical model parameters for the planning of the radiation therapy of malignant tumors. 2. A method of adjusting the mathematical model parameters for calculating the tolerance doses and probabilities of the occurrence of radiation complications in body organs and tissues].

To enhance the accuracy of calculation of tolerance doses, adequate doses and the likelihood of radiation complications in normal organs and tissues, a method has been developed for local model parameter adjustment (LMPA) by using mathematical models. It includes the analysis of the structure of a mathematical model, the systematization of clinical data and their goal-oriented use for model adjustment. The necessity of developing a new research line (LMPA) is determined by the complexity of the irradiated organism as a system and by the attempts to take into account the impact of the system on the parameters of mathematical models. LMPA can be considered to generalize determination of the parameters of mathematical models or their directed (interactive) determination. The strategy of using LMPA, which is based on the preset radiation treatment protocol and its respective dosage distributions in normal organs and tissues, is described. The efficiency of LMPA is shown to depend on the volume and relevance of clinical data that the radiological therapist has at his disposal.

Computer Simulation↗
PubMed1985

Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells.

A mathematical model of glycolysis in human erythrocytes is proposed to study the influence of a pyruvate kinase deficiency on the energy metabolism. The model takes into account the main regulatory properties of the non-equilibrium enzymes and the magnesium-complex formation by the adenine nucleotides and by 2,3-bisphosphoglycerate. In the normal case (no enzyme defect) the calculated flux rates and metabolite concentrations are in a good agreement with experimental data. It is shown that a severe pyruvate kinase deficiency manifested in a tenfold diminished activity of that enzyme leads to a remarkable decrease of the glycolytic flux and the ATP concentration of about 50% of the normal values. On the other hand a lowering of the pyruvate kinase activity to half of the normal value, characteristic for the heterozygotes, gives no significant alterations of the metabolite concentrations and the flux rates compared with the normal case which is in accordance with the lack of clinical symptoms for a metabolic disease of these probands. For three patients with known alterations of their pyruvate kinase mutants the calculated metabolite concentrations and the control characteristics permit estimation of the degree of disorder of the glycolytic pathway. The resulting classification corresponds well to other independent experimental and clinical findings. In particular, the calculation demonstrates that there is no simple correlation between the lowered enzyme activity and the reduced flux rate through the affected pathway.

Adenosine Triphosphate↗
PubMed1987

Flow characteristics of red cell containing fluids through pores. The effect of filter plugging, a mathematical model.

A mathematical model was developed that describes the effects of filter plugging on flow through 3 micron pore polycarbonate filters as a function of time, pressure, and cell concentration, both under stirring and nonstirring conditions. The mathematical constants for the model were derived from experimental data generated with a filtration apparatus, and were tested by using various concentrations of cells that are able to plug filter pores. A computer simulation program was written to test the model over a wide range of nonfilterable cell concentrations.

Blood Flow Velocity↗
PubMed1992

Determination of the mechanism of retrotransfer by mechanistic mathematical modeling.

Two mathematical models to elucidate the mechanism of retromobilization (or retrotransfer), that is, the ability of conjugative plasmids to mobilize genes into the cell containing the conjugative plasmid, were developed. This study deals with retromobilization of nonconjugative plasmids (Tra-Mob+). Plasmid transfer was modeled by two mass action models. The first is based on the hypothesis that retromobilization of the Tra-Mob+ vector occurs in one step, by means of the pilus formed by the Tra+ plasmid in the original host. In the second model, retromobilization is considered to be a two-step process involving two transfer events. The first step involves the transfer of the Tra+ plasmid from the recipient cell to the donor of the nonconjugative vector, and during the second encounter the nonconjugative vector is mobilized toward the recipient. Since the relationships between the number of transconjugants and the number of recipients for the two models are different, filter matings were performed for short time periods with different initial densities of the recipient population. Comparison of the numbers of transconjugants with the results of the mathematical equations confirmed the hypothesis that retromobilization is a one-step conjugation process.

Conjugation, Genetic↗
PubMedDate not supplied

[Oscillations and trigger phenomena in fructose-2,6-bis-phosphate metabolism. A mathematical model].

A mathematical model describing metabolism of fructose-2,6-bisphosphate (F2, 6P2), which is a powerful mediator in glycolysis, is investigated. The model takes into account inhibitory effect of F2, 6P2 and fructose-6-phosphate (F6P) on protein kinase, which phosphorylates the bifunctional enzyme fructose-6-phosphate-2-kinase/fructose-2,6-bisphosphatase. Such a mechanism of enzyme chemical modification in the presence of F2, 6P outflow from the F6P in equilibrium with F2, 6P2 cycle, caused by nonspecific phosphatases, can display trigger phenomena and sustained oscillations in F2, 6P2 metabolism and in the whole glycolytic system. The results obtained suggest that earlier models of the generation of glycolytic oscillations should be revised.

Fructosediphosphates↗
PubMedDate not supplied

Development of phage populations in a bacterial culture: a mathematical model.

A mathematical model for the interaction kinetic in phage-bacterium culture is proposed. An appropriate analytical relationship between phage and bacterial concentrations has been derived. Characteristic kinetic constants have been obtained by comparing the experimental growth curves with computer-simulation analysis. The model allows also to evaluate the phage-yield as a function of the initial concentrations.

Bacterial Physiological Phenomena↗
PubMedDate not supplied

[Double-frequency oscillation in the glycolytic system. Mathematical model].

A mathematical model describing the generation mechanism of double-frequency oscillations in the glycolytic system is proposed. Interaction of two connected glycolytic oscillation generators are put in the basis of this mechanism. It is assumed in the model that the first oscillation generator is formed due to product activation of phosphofructokinase (PFK) with adenosine diphosphate (ADP), while the second one is based on substrate inhibition of glyceraldehydephosphatededhydrogenase (GAPDH) with glyceraldehydephosphate (GAP).

Adenosine Diphosphate↗