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At least 487 records · Page 27Linked to original sources
PubMed2006

A mathematical model for predicting the outcome in moderate head injury.

BACKGROUND: Virtually all the literature on head injury has focused on the outcome prediction of severe and mild head injuries and very few studies have been dedicated to patients sustaining moderate head injuries. AIM: To identify the patient following moderate head injury who may die, develop severe disability or significant cognitive and behavioral problems on the first day of injury itself. SETTING: Tertiary teaching hospital. DESIGN: Prospective study divided into two groups. MATERIALS AND METHODS: The study included 85 patients whose Glasgow coma scale score were 9-12 and who had isolated moderate head injury. Among the above patients a preliminary prospective study was conducted in first group of 64 patients using 7 clinical factors, 18 neuro-behavioral sequel and CT brain data in prediction of outcome with moderate head injury. From the results obtained in the above study three statistically significant factors were identified and a mathematical model was developed and used prospectively in the next 21 patients and its accuracy was evaluated. STATISTICAL METHODS USED: Multiple regression analysis and Kendall's tau non- parametric test using statistical package for social sciences (SPSS 11-5-version) were used to find out the predictive factors. RESULTS: Results of these patients showed combination of CT scan brain data, verbal response and neurological signs could provide a reliable prediction in moderate head injury. CONCLUSION: Based upon the above results a mathematical model was developed giving a value for the above-mentioned factors. The mathematical model was "CT brain data x (Verbal response + Neurological Signs)". Its overall accuracy when used on the day of admission was around 80%.

Craniocerebral Trauma↗
PubMed1997

A maternal screening program for congenital toxoplasmosis in Quindio, Colombia and application of mathematical models to estimate incidences using age-stratified data.

We studied 937 pregnant women from Quindio, Colombia for the presence of specific anti-Toxoplasma gondii IgG antibodies using the indirect immunofluorescence antibody technique (IFAT-IgG). Specific anti-T. gondii IgM antibodies detected using the immunosorbent agglutination assay (ISAgA-IgM) were investigated in patients with high titers in the IFAT-IgG (dilutions > or = 1:1,024). We used mathematical models based on the age prevalence results of the IFAT-IgG to estimate the number of seroconversions and these were compared with the results predicted by the IgM based-incidence results. We found 15 positive cases by ISAgA-IgM and we were able to follow the children of six mothers from this group in which we found one case of congenital toxoplasmosis with the development of a retinal scar despite prenatal and postnatal treatment. The estimation of new cases for the annual total of pregnancies (approximately 8,000) in the Quindio region was 30-120 according to the ISAgA-IgM results and 57-85 using mathematical models. Thus, mathematical models based on age prevalence can give useful estimations of the magnitude of the problem.

Adolescent↗
PubMed1993

Fetal growth: a comparison of growth curves with mathematical modeling.

This study compared the use of fetal growth curves with the Rossavik mathematical model in predicting third trimester fetal growth in 27 Hispanic patients. The parameters tested were BPD, HC, AC, and FL. The growth curve method of predicting third trimester fetal growth was significantly more accurate than the mathematical model for three of the four fetal parameters tested: BPD, HC, and FL. We conclude that the mathematical model method offered no advantage over the more commonly used growth curve method for predicting third trimester fetal growth. In addition, growth curves do not require complex calculations and are conceptually simpler and easier to use.

Adult↗
PubMedDate not supplied

[Mathematical model of the dual action of G protein on the Ca2+ current in identified neurons of the snail Helix aspersa].

INTRODUCTION: The effect of the dopamine on the calcium current of identified cells of the snail Helix aspersa consists on an initial decrease, followed by a subsequent increase when the drug is removed. It had been previously demonstrated that this effect is mediated by a G protein, supposing that the decrease of the current would be mediated by the G alpha subunit, while the increase would be produced by the G beta gamma subunit. OBJECTIVE: A mathematical model has been developed with the object to test if the hypothesis of the dual action of the G protein could explain the experimental results. MATERIAL AND METHODS: It has been recording by means of the 'patch-clamp' (whole cell) in identified cells of snail. On the other hand, it has been developed a mathematical model of the calcium current using a Hodgkin-Huxley model, and a simulation of the action of the G protein on this current. RESULTS: Adjusting the kinetic parameters of the channel by means of the experimental data, it has reproduced in a faithful way the behavior of the calcium current. The simulation of the action of dopamine reproduces the decrease and increase of the current by means of the serial action of the G protein's subunits. CONCLUSION: Although a mathematical model cannot demonstrate the logic necessity of the hypotheses on that is based, it is unequivocally demonstrated that the hypothesis is fully compatible with experimental results.

Animals↗
PubMed1999

[Mathematical coupling and "regression to the mean". A statistical case history].

"Regression to the mean" (RTM) is a statistical phenomenon originating from the random variation of variables rather than a true association between the variables. RTM is closely linked to mathematical coupling; unawareness of these phenomena may lead to misinterpretation of data. A study examining intracranial pressure before and after infusion of manitol is presented, in which mathematical coupling caused a highly significant (but spurious) correlation between the analysed data. The significance of RTM and mathematical coupling is demonstrated by analysis of a data set derived from random numbers.

Data Interpretation, Statistical↗
PubMed2000

[HIV-1 quantitative dynamics in vivo: a review of mathematical models].

Over the last years, mathematical models have been applied in HIV infection to investigate the population dynamics of HIV-1 and cells of the immune system in infected hosts. They have contributed to a better understanding of the pathogenesis of AIDS. Among the model-based works, the quantitative studies carried out by two teams, during the years 1995, 1996 and 1997, have brought important results on HIV infection dynamics, reminding that HIV belonged to the lentivirus family, which had not been integrated in research of the previous years. In the studies on HIV dynamics, solutions of mathematical models were fitted to viral and/or immunological markers data in order to estimate the parameters of the viral and cellular production kinetics in infected patients. The present paper is a critical review of these studies. The methods and the most important results are presented. We explain why their impact was so considerable, but also show how the simplicity of modelling could result in conceptual errors. We finally discuss the contribution and the limits of mathematical models in the analysis of experimental data.

Acquired Immunodeficiency Syndrome↗
PubMed2002

The use of mathematical models in teaching wastewater treatment engineering.

Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available.

Curriculum↗
PubMed2002

Mathematical models of human CD4+ T-cell population kinetics.

We review how mathematical models help the interpretation of data measuring CD4+ T-cell kinetics by two recently-developed techniques. Mathematical models are developed for the average content of T-cell receptor excision circles (TRECs) and the average telomeric restriction fragment (TRF) in T-cells in the peripheral blood. Changes in the TRECs were supposed to indicate changes in thymic production. The rate at which naive and memory CD4+ T-cells erode their telomeres was supposed to reflect their respective division rates. Analysing the mathematical models, we show that rapid changes in the TRECs per naive T-cell are most likely due to changes in the division rates, and that the rates of telomere erosion fail to reflect naive and memory division rates. The model is applied to explain data showing that rheumatoid arthritis (RA) patients have abnormal TRECs and telomeres.

Arthritis, Rheumatoid↗
PubMedDate not supplied

All-ceramic crowns and preparation characteristics: a mathematic approach.

PURPOSE: The purpose of this investigation was to compare two mathematically calculated preparation parameters, ie, retentive capacity and finish line type, with a visual characterization based on a 3-D projection of the same prepared teeth on a PC screen. MATERIALS AND METHODS: Data from 400 teeth prepared for all-ceramic crowns recorded and manufactured by the Procera system, ie, 100 teeth each of types 11, 13, 14, and 16, were selected. Teeth were visually characterized for retentive capacity as good, acceptable, or insufficient, and type of finish line was characterized as deep chamfer, chamfer, or knife edge. For the mathematic calculations, data points located along vertical lines every 10 degrees around the tooth from finish line to occlusal/incisal midpoint were selected to calculate retentive area, defined as the part of the axial walls with an angle of less than 10 degrees to the preparation midline, and the area at the finish line with an angle of more than 45 degrees to the midline. RESULTS: Significant differences were found between the calculated size of surface areas for all types of prepared teeth visually characterized as having good retention and the two other categories (acceptable and insufficient). The difference between the latter two categories was not significant. Significant differences were also found between calculated surface areas for teeth visually characterized as having a deep chamfer and the two other finish line categories, ie, small chamfer and knife edge, but not between the latter two categories. CONCLUSION: The mathematic program allows a characterization of preparation parameters and may be further developed for use in prospective or retrospective studies of CAD/CAM restorations.

Algorithms↗
PubMed2003

The glycolytic phenotype in carcinogenesis and tumor invasion: insights through mathematical models.

Malignant cells characteristically exhibit altered metabolic patterns when compared with normal mammalian cells with increased reliance on anaerobic metabolism of glucose to lactic acid even in the presence of abundant oxygen. The inefficiency of the anaerobic pathway is compensated by increased glucose flux, a phenomenon first noted by Otto Warburg approximately 80 years ago and currently exploited for 2-fluoro-2-deoxy-D-glucose-positron emission tomography imaging in clinical radiology. The latter has demonstrated the glycolytic phenotype is a near-universal phenomenon in human cancers. The potential role of the glycolytic phenotype in facilitating tumor invasion has been investigated through mathematical models of the tumor-host interface. Modified cellular automaton and diffusion reaction models demonstrate protons will diffuse from the tumor into peritumoral normal tissue subjecting nontransformed cells adjacent to the tumor edge to an extracellular pH significantly lower than normal. This leads to normal cell death via p53-dependent apoptosis pathways, as well as degradation of the interstitial matrix, loss of intercellular gap junctions, enhanced angiogenesis, and inhibition of the host immune response to tumor antigens. Transformed cells maintain their proliferative capacity in acidic extracellular pH because of mutations in p53 or some other component in the apoptosis pathways. This allows tumor cells to remain proliferative and migrate into the peritumoral normal tissue producing the invasive phenotype. Mathematical models of invasive cancer based on tumor-induced acidification are consistent with extant data on tumor microenvironment and results from clinical positron emission tomography imaging, including the observed correlation between tumor invasiveness and glucose utilization. Novel treatment approaches focused on perturbation of the tumor microenvironment are predicted from the mathematical models and are supported by recent clinical data demonstrating the benefits of azotemia and metabolic acidosis in survival of patients with metastatic renal cancer. The evolutionary basis for adoption of the glycolytic phenotype during carcinogenesis remains unclear because it appears to confer significant competitive disadvantages on the tumor cells due to of inefficient energy production and expenditure of resources to remove the acid byproducts. We propose that the glycolytic phenotype represents a successful adaptation to environmental selection parameters because it confers the ability to invade. That is, the glycolytic phenotype allows the cell to move from the microenvironment of a premalignant lesion to adjacent normal tissue. There it competes with normal cells that are less fit than the populations within the tumor in a microenvironment of relative substrate abundance. The consequent unrestrained proliferation allows the glycolytic phenotype to emerge simultaneous with the transition from a premalignant lesion to an invasive cancer.

Animals↗
PubMedDate not supplied

[Mathematical modeling of movement of cilia in olfactory cells].

A mathematical model of the movement of olfactory cilia in different conditions was constructed. The realization of the model includes the development of a mechanical mathematical rheological model of the behavior of a continuous deformable medium, the development of the method of solution adapted to this problem, and obtaining a numerical solution, which takes into account different starting data. The mathematical modeling of the dynamic behavior of a deformable medium was performed using a system of equations for the dynamics of the deformable medium and the solution of the corresponding nonstationary system of equations in partial derivatives.

Cell Movement↗
PubMed2003

To verify four 5-year-old mathematical models to predict the outcome of ICU patients.

AIM: The aim of this study is to verify calibration and discrimination after 5 years in the case mix of patients admitted to the Intensive Care Unit (ICU) during the year 2000. In this way we want to perform a quality control of our ICU in order to justify the increased amount of money spent for intensive care. METHODS: A prospective study has been made on the 357 patients admitted to the ICU during the year 2000. The Apache II score was calculated within the first 24 hours and, depending on the length of stay in the ICU, on the 5(th), 10(th) and 15(th) day after ICU admission. On the basis of the 4 mathematical models death risk has been calculated for each of the 4 times. The Hosmer-Lemeshow test was performed for calibration and ROC curves for discrimination, always for each of the 4 mathematical models. RESULTS: The 1(st) model, at 24 hours from ICU admission, showed a bad calibration (p=0.000088), while the ROC curve was 0.744+/-0.32. Also the 2(nd) model, at the 5(th) day from admission, showed a bad calibration (p=0.000588), with ROC curve of 0.827+/-0.04. The 3(rd) model (10(th) day), was well calibrated (p=0.112247) and discriminating (ROC=0.888 +/-0.04). Finally the models at 15 days showed again a bad calibration (p=0.001422) but a very good discrimination (area=0.906+/-0.06). CONCLUSION: Developing mathematical models to predict mortality within ICUs can be useful to assess quality of care, even if these models should not be the only ICU quality controls, but must be accompanied by other indicators, looking at quality of life of the patients after ICU discharge.

Critical Care↗
PubMed2004

[Logical-mathematical "ND" software development].

In this article, we propose a mathematical analysis model for the generation of a proportional value of defining characteristics in nursing diagnoses. The study results are based on the logical-mathematical development of software specifically built for the generation of diagnosis hypotheses. The final calculation creates the sum of all defining characteristics found in each diagnosis, comparing it with the value of the V variable of the diagnosis, according to a mathematical rule that was set. It is concluded that the software needs to go through clinical validation in order to evaluate the pertinence of the rule proposed here.

Models, Theoretical↗
PubMed2004

[A comparative study on experimental and mathematical analysis of mechanical properties of PFM].

In this study we compare the experimental and mathematical analyses of mechanical properties of PFM and analyze their correlation levels and inner links. Fifteen PFM specimens with different thickness ratio of metal to porcelain are made , with the shape of 26mm x 4mm x 1.5mm, and are divided into 5 groups, the metal thickness increases with 0.05mm change each among every group from 0.25mm to 0.45mm, the porcelain thickness decreases accordingly. The three-point-fracture test is used to measure their bending strength and elastic modulus, exhibit their changing laws, and disclose their inner relationships. When the whole thickness of the specimen is determined, the fracture load, bending strength and elastic modulus increase according to the increase of the metal thickness. The experimental mechanical properties of PFM are significantly influenced by the thickness ratio of metal to porcelain, and are the same as the theoretical ones calculated by the mixed law formula of compound material. There is significant correlation between the experimental analysis and mathematical analysis of mechanical properties of PFM. The regression coefficients can be obtained to describe this relationship. Further more, they can be used as the corrected parameters of the theoretical formula. The corrected mathematical formula is helpful to predicting and improving the mechanical properties of PFM.

Compressive Strength↗
PubMed1991

Mathematical model for comparing proficiency testing results across analytical methods.

Proficiency testing (PT) programs may fail to establish a range of acceptable performance in a challenge when an insufficient number of participants use a particular method. In this study I analyzed a mathematical approach to establish acceptable performance in alanine aminotransferase (ALT; EC 2.6.1.2) PT challenges. This approach was derived from the mathematical model used in establishing a nationwide ALT standardization system for blood-collection facilities in 1988. A ratio of results was derived between each method in the PT program and an arbitrarily chosen "standard" method. The intent of this approach was to transform a target value for a challenge as determined in the "standard" method to units applicable to methods utilized less often. However, the high degree of variability over time in the ratios for some methods precluded general application of this approach. Therefore, although this simple mathematical method was successful in implementing an ALT standardization system across different methods, a derivation of this approach did not afford comparison of results in PT challenges.

Alanine Transaminase↗
PubMed1990

[Evolutionary and prognostic studies of patients with primary liver cancer. II. Multifactorial analysis using a stepped-regression mathematical model and graphics].

The subject of this study is the evolution and prognosis of 63 patients with primary liver carcinoma assessed bu multifactor regression mathematical model realized with the aid of the program 2R of the statistical package VMDR and by graphic expression of the functions of survival, mortality, speed of mortality function growth and graphic assessment of survival according to Okuda's method. The step regression analysis in 2 steps of the regression mathematical model of the clinical indices pointed out the factors age, edema and liver encephalopathy. By 7 steps in the regression mathematical model of the combined clinical and clinico-chemical indices as basic prognostic factors were selected: prothrombin time, liver encephalopathy, direct bilirubin, age, GGTP and sex.

Adult↗
PubMedDate not supplied

[Preliminary verification of a mathematical model for evaluating the operative risk in a personal caseload].

The authors applied a mathematical model of evaluation of operative risk to a group of patients undergoing general and obstetric-gynecologic surgery. They verified that all risk factors identified by this mathematical model really influenced operative morbidity and mortality in the present study too. In this univariate analysis, anesthetic technique was found to influence patients' outcome, so it must be included in multivariate analysis protocols. Therefore, this mathematical model showed to be of value in assessing operative risk factors.

Adolescent↗
PubMed1980

[Mathematical models in epizootiology].

Mathematical modelling in epizootology makes it possible to forecast the occurrence and spreading of infection, to learn the main factors of the origin and spread of infection, or to test hypotheses on these factors. Therefore epizootological models must be correct from the biological and mathematical view-point. They should not contradict to experimental facts, must be sufficiently sensitive to important factors, and must be able to approximate real epizootological phenomena and processes. Examples of the construction of simple deterministic and stochastic models of exogenous infections whose etiological agents meet the conditions of Henle-Koch's postulates are used for demonstrating the basic approaches to the use of mathematical models for the evaluation of epizootological analyses and programmes of infection control.

Animals↗