Graz Advanced School of Science, PHYSICS COLLOQUIUM OF THE UNIVERSITY OF GRAZ AND THE GRAZ UNIVERSITY OF TECHNOLOGY

Ao.Univ.-Prof. Dr. Helmut Ahammer

Institute of Biophysics, Medical University of Graz, Harrachgasse 21, 8010 Graz, Austria

Abstract:

Medical radiology as well as digital pathology produce digital images up to very high

resolutions. The number of images taken in clinics as well as pre-clinics is steadily

increasing, but nevertheless, there is a lack of quantitative or mathematical methods to

circumvent subjective misinterpretations. The theory of fractals and Non-Euclidean

geometry is well suited to describe relative complex spatial patterns of cells, cell nuclei

or tissues. In medicine and more generally in nature, fractals do not appear as exact

mathematical fractals and therefore, a statistical approach is essential. Several

methods exist and can be applied in order to calculate estimations of fractal

dimensions. Actual values are well suited to distinguish between distinct grades of

pathology, e.g. grades of pre-cancerous malformations of cell nuclei shapes.

Fractals and nonlinear deterministic dynamical systems are tightly connected and

therefore, temporal investigations in medicine are of interest, too. Particularly, the

nonlinearly affected heart rate variability is a well-regarded parameter for several heart

diseases. Current experiments using autorhythmic embryonic heart cells enable direct

investigations on a cellular level. Recent results have shown that healthy cells have a

higher beat rate variability than cells under toxic conditions.