Inverse finite element characterization of soft tissues with aspiration experiments

Abstract

In this thesis a method for the determination of material model parameters for biological soft tissues is presented. The requirement of in-vivo applicability of the method led to the development of a tissue aspiration instrument. The aspiration instrument was developed by Vladimir Vuskovic at the Institute of Robotics, whereas this work is mainly concerned with the continuum mechanical modelling of the soft tissues, the robust determination of the corresponding material model parameters, and their validity under more general loading conditions. In the first part of this thesis an explicit axisymmetric finite element formulation for the simulation of the aspiration experiment is derived and implemented. The nearly incompressible material behaviour of soft biological tissues results in very small time steps of the explicit integration and thus in computationally expensive simulations. The quasi-static character of the aspiration experiment is used advantageously to accelerate the simulations by artificially increasing the material density. The finite element code was integrated into an optimization algorithm. The optimization algorithm allows to fit unknown material parameters entering the finite element simulation to experimental reference data. Soft biological tissues are modelled as isotropic, viscoelastic, non-linear, and nearly incompressible. The continuum mechanical hyperelastic models employed are standard models in the field of biomechanics. Viscoelasticity is accounted for by a quasi-linear formulation. In view of the twodimensional data available from the experiments, the huge computational effort, that would be connected with a three-dimensional simulation, and the large increase in the number of unknown material parameters the soft tissue models are restricted to isotropic behaviour. The friction in the contact zone of the tissue with the aspiration tube proved to play an important role for the determination of the material parameters. Experiments with a simple “tribometer” for the assessment of the respective friction coefficient posed many difficulties. In numerical studies the influence of the friction coefficient on the parameter determination process was studied. As a result of these studies it is recommended to increase the friction in the aspiration experiment as much as possible to ensure sticking of the tissue to the surface of the aspiration tube. Numerical studies of the convergence properties of the optimization