Measurements and modelling of the compliance of human and porcine organs

Stress–strain data obtained from animal and human tissue have several applications including medical diagnosis, assisting in surgical instrument design and the production of realistic computer-based simulators for training in minimal access surgery. Such data may also be useful for corroborating mathematical models of tissue response. This paper presents data obtained from ex-vivo and in-vivo tissue indentation tests using a small indentor that is similar to instruments used in minimal access surgery. In addition, uniform stress tests provide basic material property data, via an exponential stress–strain law, to allow a finite element method to be used to predict the response for the non-uniform stresses produced by the small indentor. Data are obtained from harvested pig liver and spleen using a static compliance probe. Data for human liver are obtained from volunteer patients, undergoing minor open surgery, using a sterile hand-held compliance probe. All the results demonstrate highly non-linear stress–strain behaviour. Pig spleen is shown to be much more compliant than pig liver with mean elastic moduli of 0.11 and 4.0 MPa respectively. The right lobe of human liver had a mean elastic modulus of about 0.27 MPa. However, a single case of a diseased liver had a mean modulus of 0.74 MPa — nearly three times the stiffness. It was found that an exponential stress–strain law could accurately fit uniform stress test data and that subsequent finite element modelling for non-uniform stress around a small indentor matched measured force characteristics.