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Biomedical subjects

J Peil

Publications and source records attributed to J Peil.

At least 55 records · Page 3Linked to original sources
PubMed1982

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.

Humans↗
PubMed1981

[Non-statistical biomathematics: opinions, perspectives, problems].

By way of tracing the position of biomathematics and its main subjects a discussion is given of the mutual relations between the branches of natural sciences and mathematics within the hierarchically structured building of science. The general possibilities of a mathematical expressing and description of the biological features "complexity", "variability", and "discontinuity" and the limits are shown of validity of mathematical formulations in the field of biology. To this point representative opinions of research workers are quoted. The only direct ways of application of mathematics in biology seems to be the treatment of "variability" by statistical biomathematical means which offers the mathematical services in the design of experiments as well as in the quantitative-descriptive evaluation of experimental results. Aside from these ways a direct mathematical approach to biology is thought of being questionable because of the large differences between the levels of abstraction on which these two disciplines work. But the thesis is stated and supported that biophysics and biocybernetics as mediators provide an appropriate approach of the mathematics to such biological problems which arise from "complexity" and from "discontinuity". The kind of biomathematical tools, the goal of a biomathematical analysis, and the results of such an analysis get their meaning from the biophysical or biocybernetical modelling in which they are embedded. Example of working out of biomathematical methods and of application these methods are added.

Biometry↗
PubMed1981

[On the strategy of measuring in gerontology (author's transl)].

By the point counting method and empirical regression we investigated the aging changes in volume densities of histological structures in 43 human thyroid glands and in 42 human submandibular glands. Especially we wanted to show, how the change of the most important errors influences the shape of our aging curves. We had to take into consideration the statistical error, the error caused by the structural heterogenity, and the error caused by the interindividual variability. It was shown, that an increase of the exactness of measuring as well as a consideration of the structural heterogenity in the organs do not change the course of aging curves and 42 or 43 cases were sufficient for our investigations.

Adolescent↗
PubMed1980

[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. Also the possibilities are shown for application of empirical regression procedures for a quantitative characterization of the systematical component in time series of morphometrical datas and for separation of such a trend component out of the time series.

Histological Techniques↗
PubMed1980

[An ALGOL computer program for extensive automatic data processing and evaluation of karyometric studies].

A short survey is given upon ALGOL-computer programs which are ready for use also for a biomathematical treatment of morphometrical findings. Thereafter, the numerical and the nonnumerical steps are described following the caryometrical measurements. These steps are formulated algorithmically, constituting the main parts of a computer program for data transforming and evaluation of caryometrical studies by a data processing system.

Cell Nucleus↗
PubMed1979

[Quantification of environmentally influenced differences in physical and mental development of infants by a phenomenologic-mathematical separation of the body length growth into growth spurts (author's transl)].

Retardation phenomena in the physical development--especially in the increase of body length--of infants taken care of in social institutions (day-nursery, week-nursery, residential nursery) in relation to those growing up in the family will be represented in a quantitative-analytical form on the basis of a phenomenologic-mathematical model. This kind of modelling consists in the separation into 7 successive growth periods (growth spurts) of the whole growth process during the time interval from conception until the age of 3 years. For the time interval from birth until the end of 3 years we have 4 such growth spurts. The second one (fifth in the former numbering) determines mainly the growth during the 2nd year of the individual's life and makes evident the delay in the mean increase of body length of infants taken care of in social institutions, which is most evident for children who grow up in a residential nursery. The quantitative statements derived from the mathematical model concerning the physical development will be confronted with the known facts concerning the retardation in the mental-psychial development--especially in the ontogenesis of speech--of the same groups of children. There is an astonishingly close accordance of the values of time delays in reaching the levels of the physical and of the psychical development. The model may help to perceive and to diagnose the complex of causes responsible for these retardation phenomena from a social-medical and biological point of view. On the other hand this may also give a critizism and assessment of the real relevance of the biomathematical separation of the growth process into single growth spurts practiced here.

Body Height↗
PubMed1979

[The determination of the parameter of Bertalanffy's growth differential equations by means of nonlinear internal regression].

A short survey is given on various parameterized versions of the logistic law of growth and of Bertalanffy's growth differential equations. To examine the validity of these various growth expressions internal nonlinear regressions were performed, and the results of the calculations are presented. The body length growth of man within the embryonic development serves as examples of a growth process. The parameters in the differential equations will be adjusted to the course of the divided central differences calculated from means of measured values of this growth process.

Body Height↗
PubMed1979

[The description of growth course using a generalized logistic growth function].

For a quantitative description of measured growth courses the generalized logistic function will be used which is derived on the basis of the well-known logistic function of VERHULST. Numerical properties of this expression and possibilities for its computerized adjustment to measured courses are discussed. Examples of growth processes and their mathematical description by adjusted generalized logistic functions demonstrate the effectiveness of an ALGOL-program system for nonlinear approximation which is specialized to this function type. Especially the numerical improvement of approximation quality is demonstrated for expressions containing an absolute term in form of an also adjustable parameter.

Body Height↗
PubMed1979

[Quantitative mathematical evaluation of growth studies from the viewpoint of exogenously or genetically influenced variability].

Firstly, the ideas are sketched which serve as the basis for the phenomenologic-mathematical kind of modeling of the body length growth process of man. For proving the biological relevance of the spurts analyzed by numerical procedures one has to consider the social and the biological circumstances in which the growth process takes place. An analysis of longitudinal data series of the body length of (monozygotic) twins will give further hints to the possible meaning of the growth spurts by way of separation of exogenous and of genetic determined endogenous agents on the growth process. The data available for our examinations cover the time interval of the praepubertal and the postpuberal development as well as the time interval in which the puberal growth spurt takes place. The way to proceed in evaluation these time series will be presented.

Adolescent↗
PubMed1978

[Report on the round-table discussion of the subject "idea and experience" in connection with the 1977 annual meeting "process kinetics" of the German Academy of Natural Scientists Leopoldina (Halle/S., October 16, 1977)].

A report is given about a round-table-discussion upon the role and meaning of "idea and experience" in the creative scientific process. Notable representatives of mathematics, theoretical physics and geophysics, chemistry, theoretical and general experimental biology, and of medicine contribute in the discussion guided by C. F. V. WEIZSACKER to this theme from point of view of their disciplines. The components of meaning of "idea and experience" in their connection one to another may be paraphrased by such pairs of terms as "theory and practice", "theoretical or empirical", "law and appearance of a single phenomenon", "unity and diversity", abstract and concrete". It was demonstrated that in each of the mentioned scientific disciplines there is a natural, and that, starting from mathematics and going to biology and medicine, the weight in that relation will shift more and more to "experience". Many of the known methodological problems and difficulties will arise in the mentioned scientific branches if one stresses immoderately only one component of "idea and experience" by leaving the natural, discipline-related range of variation of the relation "idea and experience".

Academies and Institutes↗
PubMed1978

[Logistic law of growth and its implications].

The "morphological" (i.e. structural and quantitative) properties of VERHULST's "Logistic Law of Growth" in its versions as differential equations and as analytical functions will be discussed. It follows the attempts of generalizations of the logistic law of growth by parameterization or by changing its structure due to adding parameters. Such an additional parameter is the constant term paying regard to the level (in y-direction) on which the (growth) process may start. The second manner of introducing additional parameters is the substitution of the independent variable in its linear form by a polynomial of degree k. These generalizations will be called "generalized logistic (growth-) function". Its "morphology" will be discussed. Special points there are the use of this function as empirical expression for smoothing and quantitative description of courses of measured values (of growth variables), and the genesis of the function type as solution of a first order differential equation. "Philosophy of the generalized law of growth" means a detailed discussion of properties which could be interpreted as "time structure", and of the modelling relevancy of the differential equations resp. of the analytical function expressions which represent the versions of the generalized logistic law.

Humans↗
PubMed1977

[An algol program for the computation of empiric regressions].

An explanation is given about the meaning of empirical regression and on the domain of application of this biomathematical-statistical procedure. It may be helpful in data handling after the measurements and in a first stage of data processing especially if there is a large amount of datas. An empirical regression can provide the basis for a functional relationship analysis by giving hints for the choice of empirical mathematical functions. This will be useful and necessary in such cases where the measured values have a greater dispersion and one wants to get an analytical expression for the course of measured points. In the appendix a program listing of the ALGOL-program for empirical regression is presented. Detailed remarks are made in the text concerning the program structure, the data input and output resp. the program control parameters to enable the biological or medical user to adapt the program to their special problems without the help by a mathematician, and neither with deeper knowledge of mathematics nor with detailed insight to computer technical aspects of data processing.

Animals↗
PubMed1977

[Phenomenologic-mathematical modeling of the human-body-length growth through the analysis of growth periods and their quantitative-analytical registration].

The body height growth (of masculine beings) was modelled in a phenomenologic-mathematical manner by partitioning the time course of measured growth curve in parts every of which corresponds to a separated growth period. This partitioning was reached in a natural way so that a superposition of the single spurts yields the whole measured course. Every growth batch will be described in its time course by one term of inverse tangent function. The biological meaning and an explanation of the succession of the growth spurt as an effect of control circuits need further exploratory work. For detailed statements on acceleration phenomena concerning the body height growth this analysis gives possibilities for comparing the single growth spurts of the mean growth process of two populations in question. For measured values given by BROCK (1954) and SALZLER (1967) there are five growth periods in the time intervall reaching from time of conception until the end of the first year. Comparing the mathematical functions of the corresponding growth spurts for these two groups one can conclude that the second spurt (fetal spurt) is responsible for an increase of birth body height and the fourth for an increase of body height in the suckling age of the latter group against the former one.

Adolescent↗
PubMed1977

[Possibilities and limitations in the use of the biomathematic procedure in variability studies on man].

In an anthropomorphical variability analysis the quantitative description of deterministric changes of (morphological) growth characteristics plays an important role. Working out this component of general variability and its discrimination from the random component in the measureed values underlying the quantitative analysis can be performed by biomathematical procedures. Three groups of such procedures are presented here in a survey manner. They may be employed at different levels of data processing and for quantitative description resp. mathematical modelling of the biological process in question. There are: Empirical regression, so-called internal regression, and nonlinear regression or approximation. The advantages fo employment biomathematical procedures for evaluating and interpretation of measured values of dynamical processes are sketched for the body height growth of human beings as example. But there are also mentioned limitations of application mathematical methods and procedures in the biological area.

Adolescent↗