How to test very soft biological tissues in extension?

Mechanical properties of very soft tissues, such as brain, liver and kidney, until recently have largely escaped the attention of researchers because these tissues do not bear mechanical loads. However, developments in Computer-Integrated and Robot-Aided Surgery - in particular, the emergence of automatic surgical tools and robots - as well as advances in Virtual Reality techniques, require closer examination of the mechanical properties of very soft tissues and, ultimately, the construction of corresponding, realistic mathematical models. A body of knowledge about mechanical properties of very soft tissues, assembled in recent years, has been almost exclusively based on the results of compression, indentation and impact tests. There are no results of tensile tests available. This state of affairs, in the author's opinion, is caused by the lack of analytical solution relating a measured quantity - machine head displacement - to strain in simple extension experiments of cylindrical samples with low aspect ratio. In the paper this important solution is presented. The theoretical solution obtained is valid for isotropic, incompressible materials for moderate deformations (<30%) when it can be assumed that planes initially perpendicular to the direction of applied extension remain plane. Two astonishing results are obtained: (i) deformed shape of a cylindrical sample subjected to uniaxial extension is independent on the form of constitutive law, (ii) vertical extension in the plane of symmetry lambda(z) is proportional to the total change of height for strains as large as 30%. The importance and relevance of these results to testing procedures in Biomechanics is highlighted.