Velocity-curvature relationship of colliding spherical calcium waves in rat cardiac myocytes.

Colliding spherical calcium waves in enzymatically isolated rat cardiac myocytes develop new wavefronts propagating perpendicular to the original direction. When investigated by confocal laser scanning microscopy (CLSM), using the fluorescent Ca2+ indicator fluo-3 AM, "cusp"-like structures become visible that are favorably approximated by double parabolae. The time-dependent position of the vertices is used to determine propagation velocity and negative curvature of the wavefront in the region of collision.

[Estimation of median regression from measured values].

The median regression function is defined and demonstrated by examples. A lemma with sufficient conditions for continuity and differentiation of the median regression function is proved. Its estimation from a random sample is deduced firstly based on the empirical distribution function and secondly based on a kernel estimation with Gaussian kernels.

[Periodic local approximation for the model free description of measurement courses of biorhythmic processes--demonstration example for the selection of smoothness parameters].

Measured time series with known basic periodicity may be modelfreely evaluated by procedures of local adjusted approximation. Examples of motility time series recorded in chronobiological experiments in the seasonal course of a year demonstrate aspects of choosing values of the smoothing parameter and the resulting effects for the quantitative description of the measured variations as well as for their interpretation.

Local approximation and its applications in statistics.

For the discrete and for the continuous case, the problem of evaluating the derivatives of a function f(x) in a given interval of x is solved by local approximation method. Examples of application of the resulting numerical procedures are quoted relating the estimation of smooth function and its derivative for measured values (of a growth process), internal regression, trend elimination of time series, Bernstein polynomial, and kernel estimation of a density function.

[Biomathematical aspects of numerical evaluation and mathematical modelling of non-monotonous exponential measuring processes].

Measurements of endocrinological and pharmacological processes often yield courses of time series with exponentially saturated increasing first part followed by an exponentially decreasing part. Such measured courses may be mathematically modelled by the so-called BATEMAN function type, an expression consisting of 2 e-function terms. In this paper, the method of locally adjusted functional approximation for model-free quantitative evaluation of measured time series is sketched.

Involvement of the central nervous system in malignant lymphomas of mice.

19% of the male and 49% of the female AKR mice with spontaneously developed lymphomas show an involvement of the central nervous system (CNS) in the form of a tumor cell infiltration of the leptomeninx. A significantly higher rate of lymphomas was achieved by syngeneic transplantation of lymphoma cells (intraperitoneal inoculation) in the CNS with 87% in both sexes. Morphologically, there were no differences between the leptomeningeal infiltrations in spontaneously developed and transplanted lymphomas.

[Case studies of the use of the locally adjusted polynomial regression].

Firstly the operation mode of the procedures of local adjusted polynomial regression is explained by an artificial example of data. After that, the properties of these nonparametric estimation procedures of unknown continuous functions from measured data are demonstrated by some examples arising in experimental examinations. Especially the aspect is discussed how far the main task of separating the deterministic component from the random one in the course of measured values may be fulfilled by using different degrees of polynomials in connection with different values of the smoothing parameter.

Improvement of the method of kernel estimation by local polynomial approximation of the empirical distribution function and its application to empirical regression.

The kernel estimation of an unknown density function derived from measured values has at least one disadvantage: the second central moment of the estimated density is greater than the sample variance. This is unsatisfactory. It is possible to reduce the difference between both variances by an improvement of the method of kernel estimation.

[Model-free biomathematical analysis and description of correlations].

Modelfree methods for nonparametric estimation of unknown continuous functions from measured values and their advantages as against fitting of analytical expressions are discussed. The main features are stated especially of the empirical regression and of the local adjusted polynomial approximation. These topics and problems of application of the procedures are illustrated by 3 examples coming from chronobiological, neuromorphometrical, and histochemical examinations.

[Behavior of HDL cholesterol and the apoproteins A1 A2 and B in the central circulation in patients with coronary disease and genetically determined hyperlipoproteinemias].

Seven lipid parameters, including apoproteins A1, A2 and B were determined in blood from different parts of the cardiovascular system in two groups of patients one with and the other without coronary heart disease. In addition, HDL cholesterol levels were compared in patients with coronary heart disease and primary monogenic combined hyperlipoproteinaemia. None of the seven parameters showed significant differences in samples from the pulmonary artery (mixed venous blood) and the hepatic vein of the control and patient groups.

[Procedures of local approximation for nonparametric estimation of unknown continuous functions from given measurements].

There exists a lot of literature about the nonparametric estimation of unknown continuous functions from measured values. Many formulas of different shape were discussed. In this paper, we show that a great part of those formulas may be developed by using a uniformly mathematical principle which we name the local approximation by the least squares method.

[A new procedure for estimating the distribution of measured values--demonstrated by morphometric examples].

The local approximation of the empirical distribution function of a one-dimensional continuous random variable leads to a continuous estimation of the distribution function. The first derivative of it gives the estimation of the density function. At a sample of growth data the advantages will be demonstrated of the continuous estimation compared with the classical approaches by histogram or frequency polygon respectively.

[Nonparametric estimation of 1-dimensional continuous distribution density functions using the continuous LOLINREG approximation].

A nonparametric method for estimation of one-dimensional continuous probability distribution functions is presented. Procedures for calculation of estimation of the unknown distribution function and the distribution density will be discussed in their application. 2 items are what type of weight function may be chosen for the proposed local-linear continuous approximation of the empirical distribution function by the least squares method (LOLINREG), and upon what value of bandwidth- or smoothing parameter one optimally should settle.

[A method of non-parametric evaluation of one-dimensional continuous distribution density].

A continuous density function f(x) of a one-dimensional continuous random variable X is estimated from independent measured values xi, i = 1 (1) n, by a nonparametric procedure. If the measuring precision is sufficiently high, then the density estimation f(x) will be received from the 1st derivative of the LOLINREG-approximation of the empirical distribution function which is generated by the measured values. If the measured values are granulated by a lower measuring precision, then the density estimation f(x) may be obtained from the 1st derivative of the LOLINREG-approximation of an empirical distribution function which is calculated from the natural histogram by integration.

[Locally adjusted linear regression and its possibilities for application].

A new numerical method is presented for a model free representation of the mean course in a series of measured data of an unknown functional connection. The usefulness of the method is demonstrated by some examples of different time series (chemical reaction kinetics, growth, damped oscillations of a physiological system, pharmacokinetics). The advantages of the new method compared with nonlinear regression or segmented linear regression are noted.

[Lipid chemical parameters and incidence of genetically determined hyperlipoproteinemias in patients between 20 and 45 years of age with coronary heart disease].

In 35 patients at the age between 20 and 45 years with a manifest coronary heart disease various lipid-chemical parameters were established and compared with a control group of the same age of laboratory-chemically and clinically inconspicuous test persons as well as with a group of patients with infarction older than 45 years. For HDL-cholesterol, LDL-cholesterol as well as LDL significant differences of the mean value were the result in the group of juvenile patients with a coronary heart disease and in the healthy control group as well as the group of older test persons with infarction, which confirm the accumulation of lipid-chemical risk constellations in "juvenile" patient with a coronary heart disease. Moreover, the proportion of primary hyperlipoproteinaemias is essentially greater in these patients than in older test persons with infarction.

Empirical regression for trend elimination and smoothing of time series 1,2,3.

The mathematical background of empirical regression its meaning, and its role in a first stage of data evaluation will be sketched. In the second part, applications of empirical regression procedures for time series analysis will be presented, especially for a model-free quantitative description of the trend component in nonstationary time series and for trend elimination with regard to a further spectral, decomposition and spectral characterization of the modified time series.

[Morphometric studies of the aging of human submaxillary glands (author's transl)].

Morphometric examinations were made on hematoxylin-stained paraffin sections of 43 human submaxillary glands, in order to determine and describe histological changes of this organ during the aging thereof. The number of fat cells per unit area increases in the first decades, whereas that of the striated ducts decreases. Obviously, striated ducts differentiate earlier than serous acini, with the former thus being less subject to involution with aging than the latter.

[Empiric regression as a method for "parameter-free" refining and evaluation of morphometric data for functional stochastic relations between random variables].

The statistical resp. numerical procedures of empirical regression give an objective and prejudice-free possibility for quantitative description of functional-stochastic connections between random variables. This will be explaned by heuristical arguments illustrated at an example of histophotometrical measurements.

[Bicycle ergometric testing in the acute phase of liver disease with particular reference to changes in serum enzymes].

It is reported on 20 patients (17 women, 3 men) who had undergone a bicycle-ergometric load in the acute phase of virus hepatitis (an average at the 16th day after admission to hospital). Among the significant changes of the activity the slight increase of SGPT 30 minutes after the end of the load as well as the clear decrease of the enzyme activities of SGPT and SGOT below the initial value 48 hours after load are particularly to be emphasized. LDH and CPK exhibited only insignificant changes of activity.