Quantitative Description and Mathematical Modelling of Biological Systems by Means of Nonlinear Approximations – Demonstrated at the Example of the Body Length Growth of Man

After general remarks upon the biomathematical tasks of quantitative description or mathematical modelling of biological systems and phenomena on different levels of organization the growth process of body length of human beings serves as illustration of the possibilities of such mathematical treatments. A short survey is given about the attempts of using differential equations for reflecting basic principles of growth processes. Further on analytical functions (as the solutions of growth differential equations) preferably may be used for an objective quantitative reproducing of measured courses of growth variables. The values of parameters contained in such expressions will be calculated by nonlinear fitting procedures. In nearly all cases we got a very high numerical precision in approximating parts of the body length growth process of man which extends from conception until the age of 18. Our attempts of a phenomenologic-mathematical modelling of this growth process mean a subdividing of the whole process in single growth spurts with a symmetric-sigmoidal shape of their courses, and describing the single spurt by a hyperbolic tangent function. An advantage of this kind of modelling is the fact that each of the terms is valid for the whole time interval of growth. Within the process of forming the model heuristical hints are taken into consideration arising from biological background and which would supply the possibility of interpretation and verification of the analyzed growth spurts.