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At least 739 records · Page 41Linked to original sources
PubMed1976

[Labeled mitoses curve in different states of cell proliferation kinetics. 2. Mathematical model with the calculation of transient processes].

The available information about the temporal patterns of labelling and mitotic indices in the same system has been used to develop a general approach to the mathematical simulation of labelled mitoses curve. Such states of cell proliferation kinetics as induced DNA synthesis, steady (in narrow sense) state and diurnal rhythm of proliferative processes are investigated in a greater detail. The principle of a mathematical description of an additional DNA synthesis stimulation coming from the states under consideration is also discussed in this work.

Cell Division↗
PubMed1999

[1899: the first mathematical description of the pressure-volume diagram by Otto Frank (1865-1944)].

Not until 60 years after 1899 Otto Frank's mathematical formulation of the volume-pressure diagram and his concept of the mechanism of the cardiac work of the left ventricle cardio-physiologists began to rediscover Frank's work systematically. Frank's scientific development proves his constant commitment to and deep interest in understanding and analysing physiological problems mathematically. Consequently Frank worked on the quality and theory of physiological instruments and the problems of measurement, to calculate the influence in experimental research of the cardio-vascular system. Besides Frank's publications on different types of manometers his theory of "Windkessel" function as a model of the mechanics of the left ventricle and the different energies of the cardiac work are of importance even today, although we know only few details of his life as a pupil of Carl Ludwig and Carl von Voit and as a professor of physiology in Giessen and Munich.

Blood Pressure↗
PubMed2001

The apical angle: a mathematical analysis of the ellipse.

BACKGROUND: The elliptical excision is a common surgical procedure. The dermatologic literature predominantly describes an excisional geometry with a 3:1 length:width ratio and an apical angle of 30 degrees. OBJECTIVE: To analyze the elliptical excision by applying mathematical principles and define the apical angle and its relationship to the length:width ratio. METHODS: We examined numerous examples of elliptical excisions as presented in the dermatologic literature. We analyzed the geometry of the excisions and defined it mathematically. RESULTS: The apical angle of a 3:1 elliptical excision is not 30 degrees. The true apical angle varies from 37 degrees to 74 degrees depending on excisional geometry. CONCLUSION: The commonly presented apical angle of 30 degrees is incorrect and does not reflect the true apical angle of elliptical excisions.

Dermatologic Surgical Procedures↗
PubMed2001

[Clinical importance of assessment of collateral capacity in the circle of Willis. Benefit of a mathematical blood flow model for the every-day practice of vascular surgery].

UNLABELLED: Collateral capacity of the Willisian arteries is of clinical importance during and after carotid endarterectomies. AIMS: Assessment of cerebral hemodynamics using a flow circulation model based on a mathematical formula. PATIENTS AND METHODS: Four patients suffering from ischemic stroke in moribund stage were investigated using transcranial color-coded duplex sonography. By compressing the common carotid arteries, the function of the Willisian collaterals was assessed. After the death of the patients, the circles were removed, the diameters and lengths of the arterial segments were measured. The data were analysed with the mentioned circulation model. RESULTS: The diameters of non-functioning collateral arteries were 0.4 mm, while that of the functional ones were 0.7 and 0.8 mm, respectively. In the two cases where the anterior communicating arteries did not function, a near-critical hemodynamical status was found in the end-arteries. This was especially true if the mean arterial blood pressure was 70 mmHg. The most critical hemodynamical status developed in case 4, where internal carotid occlusion on one side, a contralateral severe carotid stenosis and a non-functioning anterior communicating artery were observed. CONCLUSIONS: A special flow circulation model based on mathematical formula enables the calculation of the cerebral blood flow in the different arterial segments of the circle of Willis. Further studies are needed to clarify whether the method can be used for preoperative modeling of the cross-clamping phase of carotid endarterectomy.

Blood Flow Velocity↗
PubMed1975

Quantitative evaluation of hemodialysis therapy using a simple mathematical model and a programmable pocket calculator.

1. A single pool mathematical model has been clinically tested and found to give values similar to those previously reported for volumes of distribution of creatinine and urea. 2. Calculated generation rates for creatinine and urea approximated values obtained by independent measurement of removal rate. 3. Preliminary observations suggest that the model may be empirically useful in predicting interdialytic serum creatinine urea concentrations. 4. The potential clinical usefulness of the mathematical model has been enhanced by development of a solution suitable for a programmable pocket calculator.

Adult↗
PubMedDate not supplied

[Cerebral mechanisms of mathematical thinking].

OBJECTIVE: To suggest a cerebral map of elementary mathematical thinking, and integrate the most relevant findings from neuropsychology with those from cerebral imaging techniques and cognitive behavior experiments. DEVELOPMENT: Firstly we describe investigations into our numerical sense and the way in which numerical information is represented in the human brain. Then, using a multidisciplinary approach, we present the results of different studies of Gerstmann's syndrome, regarding the relation between numerical ability and other cognitive skills; the different participation of the cerebral hemispheres and the special implication of the parietal lobe in mathematical tasks. CONCLUSIONS: Different cerebral regions are involved in doing mental arithmetic, however simple. This makes one think more in terms of cerebral circuits than in a phrenological idea which would assign the responsibility for arithmetical calculations to a specific region. The similarity between the results analysed leads us to the conclusion that one region is particularly involved in understanding numbers, namely the inferior part of the parietal lobe. Different neuronal circuits are used depending on the type of task to be performed. Finally we describe the most relevant models for the processing of numbers which have been developed during the study.

Brain↗
PubMed2001

[Mathematical description of human root canal curvatures].

There is a necessity of a mathematical formula for the description of root canal curvatures. The aim of this study was to give a mathematical description of root canal forms. The measurements of 60 roots were conducted on isometric radiographs taken from the clinical view. Seven points of the imaginary axis were approximated using fourth-degree polynomial functions. Fourth-degree approximation for the description of the shape of root canal curvatures proved to be exact and reliably repeatable. This method may serve the classification of root canal forms as well as the description of the spatial curve of root canals.

Dental Pulp Cavity↗
PubMed2002

[Mathematical classification of root canal curvature of human teeth].

Endodontic research requires a mathematically based classification method of root canal forms. The aim of this study was to give a mathematical description of root canal forms using differential geometrical pattern analysis and computer graphics. The measurements of 433 extracted human roots were carried out on isometric radiographs taken from clinical view. Seven points of root canal axis of the same radiographs were approximated using fourth degree polynomial functions describing the imaginary axis of canals. The Schneider's angle of each root was also measured for grouping the samples according to this parameter. The classification of root canal form on the basis of Schneider's angle differs from the classification of geometrical pattern analysis. This type of classification of root canals is suitable for standardizing test specimens, including natural human teeth used for testing root forms: I (straight), J (apically curved), C (continuously curved) or S (multicurved).

Computer Graphics↗
PubMed2000

Construct validity of scores/measures from a developmental assessment in mathematics using classical and many-facet Rasch measurement.

Data from a developmental assessment comprised of 9 short answer mathematics tasks were validated using classical and three-faceted Rasch measurement methods. Field test data from a mixed age elementary school sample (N=280) were analyzed. Descriptive statistics on scores from the overall scale and two subdomains indicated improved performance with age. The data showed better fit with a two-factor model corresponding with the subdomain structure (Bentler's CFI=.94), than a one factor model (CFI=.87). The inter-factor correlation was.76. Convergent validity coefficients of scores with scaled scores of the Stanford AchievementTest mathematics battery ranged from.28 to.47; internal consistency reliability of the total and subdomain scores ranged from.87 to.89, respectively; and median inter-rater reliability was.75. On average, persons, tasks and raters showed acceptable fit with the three-facet Rasch model. Rasch logit difficulties of tasks suggested an ordered scale structure, although tasks tended to have high difficulty levels. The original and calibrated task ordering was consistent at the extreme ends of the scale. Gaps identified on the Rasch item map suggested a need for additional task construction. Conceptual and procedural differences in each technique are considered in deciding future improvements to the scale.

Aptitude Tests↗
PubMed1984

[Multidimensional mathematical demography: a survey].

The development of multidimensional mathematical demography and its application to the analysis of such changes in life status as marriage, occupation, and migration is discussed. "This article presents an overview of the methods and models specific to this new branch. It stresses (1) their relationship with the methods and models of classical mathematical demography, (2) their field of application, (3) their elaboration, and (4) a few methodological and empirical questions raised by their use." (summary in ENG, SPA)

Demography↗
PubMed1984

Estimation of mean age at first marriage: use of a simple mathematical model.

"The present paper is an attempt to introduce a simple mathematical model to describe the age pattern of proportion never married women. The underlying model was found to give fairly close fit to an observed set of data of some 17 WFS [World Fertility Survey] countries. A mathematical formulation was then suggested in terms of the parameters in the model to estimate the mean age at first marriage. The mean ages obtained under the approach agreed quite closely with those obtained by Hajnal's method. The agreement between the estimates of ever married proportions obtained by the suggested model and...Coale's nuptiality model appeared also to be satisfactory."

Age Distribution↗
PubMed2003

[Integral mathematical parameters of a gemogram as criteria for evaluation of severity of chronic adnexitis and of treatment efficacy in conservative therapy].

A number of hematological indices of the peripheral blood in patients with chronic adnexitis were mathematically calculated to evaluate a disease severity and an effect of recovery by using the traditional therapy method. It was established that the integral-and-mathematical indices of hemogram reflect clinical disease acuteness while receiving patients to hospital. A comprehensive evaluation of hematological indices makes it possible to determine the severity of inflammatory process in women, to detect the efficacy of a conducted therapy and to choose a strategy for further metabolic correction to ensure a maximum treatment effect.

Anti-Infective Agents↗
PubMed1992

[Mathematical model of oblique three-dimensional intertrochanteric detorsion varus-forming osteotomy of the femur by the Bernbeck method in surgical treatment of congenital hip dysplasia in children].

Whenever the conservative procedure fails to bring about congruence of the dysplastic hip joint, an operative procedure becomes indispensable. In Orthopaedic Clinic of the Pomeranian Medical Academy in Szczecin we implement the oblique three-dimensional intertrochanteric detorsion and varus forming osteotomy after Bernbeck in order to correct the proximal end of the femoral bone. Precise determination of the plane to be cut, prior to the operative procedure, simplifies and shortens the operation itself and facilitates the achieving of the planned angular values in all three planes. Mathematical model of osteotomy according to Bernbeck considering required angles of correction as well as angles determining the plane of osteotomy was worked out. In collaboration of the Szczecin Technical University, a simple computer program was elaborated which allowed the presentation of the results in the form of tables. With the help of tables the optimal cutting plane was chosen and created correct biomechanical and anatomical conditions as well as optimal conditions for stable osteosynthesis of dissected fragments of the femoral bone. That type of osteotomy is useful in most operative correcrions of the dysplastic hip joint (not great varus formation connected with relatively extensive detorsion). The achieved congruence in the 22 dysplastic hip joints operated on was the most important condition for their later physiological development. Short post-operative observations confirm the value of described mathematic model.

Acetabulum↗
PubMed2003

[Mathematical simulation and estimation of stress deformed status of a maxillodental segment after tooth depulpation].

Mathematical simulation, estimation, and evaluation of stress-deformed status of bone tissue under the roots of functionally loaded mandibular abutment teeth after their depulpation were carried out. The resultant mathematical model, realized in the SPLEN-K system, is the key stage in the development and subsequent clinical application of automated diagnosis and consultation complex for patients with dentition defects.

Computer Simulation↗
PubMed2003

Mathematical models of HIV and the immune system.

I describe how mathematical models have been used to elucidate the principles which govern HIV and immune system dynamics in relation to antiviral drug therapy. The review starts by introducing a basic model of virus infection and demonstrates how it was used to study HIV dynamics and to measure crucial parameters which lead to a new understanding of the disease process. Since this analysis indicates that eradication of the virus is not feasible during the lifetime of the patient, I continue to discuss mathematical models with the aim to explore how drug therapy can be used to induce long-term immunological control of the infection.

Allergy and Immunology↗
PubMedDate not supplied

[Mathematical processing of the keratograms].

The paper deals with the mathematical processing of keratograms of a new keratoscope designed by the authors. A method of describing the curve of the corneal surface section (to a certain degree) by polynomial is under consideration; the method's accuracy is assessed. The calculations' results reveal a practical suitability of the methods for measuring and for the mathematical processing of keratograms.

Corneal Topography↗
PubMed2003

Mathematical models for the evaluation of antibiotic resistance in hospitals: a systematic review.

As the appearance and spread of antibiotic resistance is becoming an increasingly serious public health problem, there is a definite need for further studies by simulation, experiment and observation. Mathematical models may provide very useful tools to develop a rationale to extend the effective life of existing and newly introduced antimicrobial agents. In this work we systematically reviewed a number of mathematical models recently presented in the literature, in order to provide a brief and informative tool for public health policy makers, regarding the spread of antibiotic resistance, worldwide.

Bacteria↗
PubMed1992

[Mathematical modelling of open-wedge tibial osteotomy and correction tables].

This study analyzes mathematically the orientation of the superior tibial epiphysis in frontal and sagittal planes for knees with genu varum arthrosis. The assessment of the opening is determined mathematically for the osteotomies; this leads to the establishment of tables which can be used in practise during upper tibial osteotomies.

Humans↗