Viscoelasticity of biological materials - measurement and practical impact on biomedicine.

Mechanical behavior of biological structures under dynamic loading generally depends on elastic as well as viscous properties of biological materials. The significance of "viscous" parameters in real situations remains to be elucidated. Behavior of rheological models consisting of a combination of inertial body and two Voigt's bodies were described mathematically with respect to inverse problem solution, and behavior in impulse and harmonic loadings was analyzed. Samples of walls of porcine and human aorta thoracica in transverse direction and samples of human bone (caput femoris, substantia compacta) were measured. Deformation responses of human skin in vivo were also measured. Values of elastic moduli of porcine aorta walls were in the interval from 10(2)kPa to 10(3) kPa, values of viscous coefficients were in the interval from 10(2) Pa.s to 10(3) Pa.s. The value of shear stress moduli of human caput femoris, substantia compacta range from 52.7 to 161.1 MPa, and viscous coefficients were in the interval from 27.3 to 98.9 kPa.s. The role of viscous coefficients is significant for relatively high loading frequencies - in our materials above 8 Hz in aorta walls and 5 Hz for bones. In bones, the viscosity reduced maximum deformation corresponding to short rectangular stress.

[Rheologic properties of viscoelastic materials--identification of models and estimation of parameters]. / Reologické vlastnosti viskoelastických teles--identifikace modelu a odhad parametru.

The methodology of description and quantification of mechanical properties of visco-elastic materials is particularly important for drug production as well as for pharmaceutical applications. Of similar importance is this methodology for biomechanics and other biological disciplines, as many biological materials belong to the category of visco-elastic bodies. Methods derived from the theory of elastic bodies or hydrodynamics are not adequate for the quantification of mechanical properties of these materials. Application of more general rheological methods is necessary in these cases. In rheology, the so-called creep curves are most frequently used as a source of information on the mechanical behavior of visco-elastic materials. Further, for more exact analysis, rheological models are often derived from the creep curves. Classical methods of identification and parameter estimation of rheological models are not sufficiently general and do not derive all information involved in creep curves. A significant contribution is the application of the general theory of systems, theory of system identification, and mathematical methodology of Laplace transformation to this field. Practical application of these methods is often relatively simple. The paper presents the necessary theoretical background and a practical guide for utilization of this methodology.

[Determination of biological age--a group of biophysical tests]. / Merení biologického veku--biofyzikální soubor testu.

BACKGROUND: Biological age is defined as real state of organism with respect to the processes of aging. From the gerontological point of view, the methodology of determination of biological age is a tool for verification of theories. The role of biological age determination in medicine is wide. It consists, among others in the assessment of the efficiency of anti-aging interventions or in detection of premature aging. Many different batteries of methods for the measurement of biological age were developed till now. The currently applied methods are not standardized and they are, as a rule, significantly time-consuming. METHODS AND RESULTS: The goal of the work was to develop a routine method for biological age determination. Simplicity and reproducibility of measurements was stressed. The result of our work is a set of 7 biophysical methods. Some of the methods are newly developed (measurement of rheological properties of the skin), others are modified classical methods (measurement of accommodation of eye, perception of high frequencies of sound, reaction times). CONCLUSIONS: The battery of biophysical test for the routine biological age assessment was developed in our laboratory. The information is processed by computer, using multiple linear regression analysis for obtaining the best assessment of personal biological age. The duration of measurement is roughly 120 min.

Gompertz - A program for evaluation and comparison of survival curves.

Principles, properties and use of a program for evaluation of survival curves are described. Parameters of Gompertzian mortality curves are computed from survival data of two populations by help of nonlinear regression. The differences in parameters of both curves are evaluated statistically. This method evaluates effectively even survival data of very small populations. The results are presented in numeric, verbal and graphic forms. Finally, reading of the results is offered to distinguish changes corresponding to altered aging rate from changes caused by influences not affecting the basic mechanism of aging. Program GOMPERTZ in the form of Microsoft Excel workbook equipped with Visual Basic procedures is offered free through e-mail (klemera@faf.cuni.cz).

[Methods of verification of aging theories]. / Metody verifikace teorií stárnutí.

The methodology of verification of theories of aging belongs to the most crucial problems in theoretical and experimental gerontology. Extensive number of hypotheses of the nature of the basic mechanisms of aging exists on the field of theoretical gerontology. This situation claims the development of the effective methodology of verification. Traditional ways of the verification were indirect and insufficient. The progress in theoretical gerontology provides the possibility to verify the theories in more exact way. Survey of the contemporary state in the theories of aging and available methods of verification is presented in the paper. The tools of verification derived from survival curves and mortality curves are analyzed and discussed. Further the tools of verification derived from biomarkers of aging and batteries of biological age are presented.

The effect of antioxidants and dietary restriction on mortality curves.

The full exploitation of information contained in mortality curves offers a tool for direct verification of theories of aging. We have analyzed the behavior of mortality curves for middle and high age groups and have proposed a mathematical model of mortality correlated with the rate of aging. The model offers an explanation for the mutual relationships between mortality curves and suggests potential methodologies for determining experimental modification of the rate of aging. The applicability of this theory is demonstrated by analysis of the changes in mortality as it is influenced by dietary antioxidants or by a calorie restricted diet. Survival data taken from a variety of studies were used as primary information, with parameters of mortality curves being determined by computer-assisted analysis of the curves. These analyses support the hypothesis that a dominant role for free radicals exists in the control of aging in Drosophila. However, in mammals-mice and rats, the effects of antioxidants as well as caloric restriction on mortality curves do not indicate that these treatments alter the rates of aging.

Changes in mechanical properties of skin as a marker of biological age.

The development of the methodology of biological age assessment belongs to the main direction of the research in contemporary gerontology. The sets ("batteries") of tests for biological age assessment involve also large number of typically biophysical measurements. For example measurements of accommodation range, visual acuity, audiometry, vital capacity, blood pressure, pulse frequency and many others. Measurement of skin elasticity is also included in batteries for biological age assessment in many laboratories. As mechanical properties of the skin belong to the quantities strongly modified by aging, they are potential biomarkers of biological age. Unfortunately, the currently applied methods are dubious from metrological and biophysical points of view for many reasons. As a rule, the time of diminishing of some type of deformation is used for this purpose. The subjective errors are present in considerable extent and interpretation of results is also difficult. Above it, this type of measurements is usually called measurement of skin elasticity but, in fact, the process of diminishing of deformation does not depend only on elasticity but depends significantly also on plastic properties of the skin. In our laboratory we suggested and verified methodology which may eliminate the problems discussed above. The methodology is based on theory of viscoelastic bodies. The principle of the methodology is as follows. The human skin (in vivo) is exposed to constant force for limited time. During the same time and after the deformation of the skin is measured. The resulting curve (creep curve) is dependency of deformation on time. The rheological model of the mechanical properties of the skin can be derived from this curve. The model consists of serio-parallel combinations of two elastic (Hooke's) and two plastic (Newton's) bodies. Rheological parameters of these bodies depend on age. The best marker of biological age prove to be modulus of Hooke's body, which is responsible for rapid phase of elastic response. The creep curves were measured in group of 69 persons of both sexes. The age range was between 25 and 82 years. The elastic modulus of Hooke's body responsible for rapid response was calculated in all cases. Further the following measurements was performed in all persons in experimental group: range of accommodation, threshold of hearing of high frequencies of sound (pitch ceiling), vital capacity of lungs, systolic and diastolic pressures of blood (in rest and after exercise), reaction times on visual and acoustic signals. All these markers where evaluated and compared. The following two parameters were taken into account: relative change per one year and coefficient of correlation. The elastic modulus proved to be marker of biological age of the similar quality as accommodation range, pitch ceiling and vital capacity and better than blood pressures and reaction times. The suggested methodology of measurement of mechanical properties of skin seems to be new, well defined biophysical marker of biological age.

Human mortality at very advanced age might be constant.

An attempt was made to identify the course of the mortality rate at the upper tail of human age. The only known data suitable for this purpose were published by Riggs and Millecchia (J.E. Riggs, R.J. Millecchia, Mech. Ageing Dev. 62 (1992) 191-199) and our analysis follows up their results. By means of mathematical elaboration it was proved that these data imply a constant mortality rate (approx. 25% per year) at ages above 113 years for men and above 116 years for women. Indirect arguments supporting the validity of the source data are discussed. Nevertheless, even if the source data are mistaken, we proved they cannot be the product of purely random errors and our results may contribute to the elucidation of the origin of those systematic errors.

Practical methodology of evaluation of mortality curves and detection of aging-related interventions.

A practical and simple method of direct proof of occurrence of changes in the aging rate is suggested. The aging rate is defined here according to the pacemaker concept of the control of aging as the rate of pace of the inner aging clock. The principle of the method consists of the analysis of relationships between mortality curves. The methodology makes it possible to distinguish the changes in mortality caused by direct intervention in the basic mechanism of the control of aging processes (the pacemaker) from changes caused by intervention in other systems of an organism. As mortality curves are often difficult to obtain directly in experimental gerontology, a method of transformation of survival data into mortality curves is demonstrated. The general purpose of this study is to derive more information from experimental data and from demographic studies, and contribute to a more exact methodology of verification in gerontology.

[Animal models in pharmacy--ethical problems and alternative methods]. / Zivocisné modely ve farmacii--etické problémy a alternativní metody.

Many fields of natural sciences still in the recent past were based almost exclusively on tests carried out on experimental animals. For the reason of protection of experimental animals, the advanced states have introduced legislative measures aiming to decrease their numbers and stressing the development of alternative possibilities of obtaining relevant results. The alternative methods usable both in the field of research and in teaching include physico-chemical methods, mathematical and computer methods, studies on lower organisms, on vertebrates in early stages of their development, on humans, and the well elaborated in vitro methods. The paper also surveys the present-day possibilities of using alternative methods in the field of organizational-informational systems, teaching and research, with concrete examples of application. The future and prospects of alternative methods as well as the present state of the art in the Czech Republic are discussed.

Influence of aging rate change on mortality curves.

One of the key problems of experimental gerontology is that there is usually some degree of uncertainty in the correct interpretation of experimental or observational data. Namely, it is difficult to decide whether the changes in life span, mortality rate or physiological state are due to the changes in biological age of organisms or to other causes. The analysis of mortality curves, suggested here, can reveal relevant information and may also contribute to discussions on the nature of the aging process. Our models are designed to provide a mathematical and system-theoretical basis to this methodology. The conditions of the validity of the models are simple and their relevancy to reality is discussed. Further, the reliability model suggests an explanation of apparent discrepancy between constant relative decline in physiological functions, often observed during aging, and Gompertzian growth of mortality.

[Stimulatory effects of small doses of mutagens]. / Stimulacni úcinky malých dávek mutagenu na organismus.

Small radiation doses stimulate the organism. This so-called hormetic effect was first described in the fifties, however, only in recent years it has been accepted. According to data in the literature the hormetic effect comprises stimulation of the immune system, a general increase of the resistance of the organism, a reduced risk of cancer and in model organisms a protraction of the median life span was observed. Positive effects of small doses were observed in experiments with cell and tissue cultures of animal and plant origin. A prolongation of the median and maximal life span in Drosophilae was also observed. There are indications that the hormetic effect could be due to the action of chemical mutagens. Attempts to explain this phenomenon are as a rule based on the finding that the activity of reparative DNA systems is substantially increased in case of a disorder of newly synthetized DNA. This reduction is triggered by a feedback reaction in the regulatory chain of synthesis of reparative enzymes. In the literature experiments were already described on the application of the hormetic phenomenon in therapy. Wider use calls, however, for systematic research. The perspective seem promising.

Theory of reliability, biological systems and aging.

The paper deals with possibilities and prospects of application of reliability theory in biology and particularly in gerontology. The possibilities and limitations of existing reliability methods are analyzed with respect to their eventual use in biology, and new methods suitable for analysis of changes in the reliability of biological systems during their aging process are searched for. A new method is proposed for reliability parameter estimation of elements and subsystems forming biological systems. Application of the method could bring new information regarding the causes of declining reliability of biological systems during their aging. Application of the method is demonstrated by an analysis of reliability of the human organism, and the results are compared with some current theories of aging.