Mechanical impedance of biological materials: concept, meaning, applications and measurement

Stanislav Ďoubal¹ (doubal@faf.cuni.cz), Petr Klemera¹, Vladimír Semecký²

¹Department of Biophysics and Physical Chemistry, Charles University in Prague, Faculty of Pharmacy in Hradec Králové, Czech Republic,
²Department of Biological and Medical Sciences, Charles University in Prague, Faculty of Pharmacy in Hradec Králové, Czech Republic

Summary

The quantitative methodology of assessment of mechanical behavior of visco-elastic materials is of crucial significance, among others for pharmaceutical technology, research in cardiovascular system or for mechanical matching of implants. The mechanical (rheological) properties of visco-elastic materials involve elastic as well as plastic elements. The mechanical behavior of these materials is non-linear in many respects and it is different in cases of static and dynamic loading. Consequently, the satisfactory description of mechanical behavior of biological materials is extremely difficult. The classical approach based on theory of elastic or visco-elastic bodies often fails to provide adequate tools for solution of these problems. The concept of complex mechanical impedance enables more universal and more adequate description of mechanical behavior of this category of materials. The concept of mechanical impedance is analogical to the concept of impedance in theory of electric circuits. The mechanical impedance is complex number defined as ratio between instantaneous complex values of stress and strain in steady state of cyclic dynamic loading. The mechanical impedance enables to calculate the amplitude as well as phase of strain response and solve the problem of mechanical matching. The theory of complex mechanical impedance as well as the methodology of identification of mechanical models of visco-elastic materials is presented in the paper.