Modelling of Brain Tissue Mechanical Properties: Bi–Phasic Versus Single–Phase Approach

摘要

Recent developments in Robot–Aided Surgery — in particular, the emergence of automatic surgical tools and robots — as well as advances in Virtual Reality techniques, call for closer examination of the mechanical properties of brain tissue. The ultimate goal of our research is development of corresponding, realistic mathematical models. The paper discusses two candidates for tissue models: standard, non–linear, bi–phasic and single–phase, non–linear, viscoelastic. The mechanical behaviour of brain tissue is highly non–linear. The stress-strain curves are concave upward containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffens as the loading speed increases, indicating a strong stress–strain rate dependence. The standard methods of modeling tissue as a bi–phasic continuum face serious problems: strong stress–strain rate dependence can not be easily explained. According to our experiments, for brain tissue the stresses under fast loading can be six times higher than those under slow loading. Therefore, the use of the single–phase model is recommended. The non–linear, viscoelastic model, based on strain energy function with time dependent coefficients has been developed. The material constants for the brain tissue have been evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. One advantage of the proposed constitutive model is that it is not difficult to be employed in larger scale finite element computations.