Comparative two- and three-dimensional finite element modelling techniques for tibial fractures

Abstract

Often the choice of a two-dimensional modelling approach over a three-dimensional approach is made on the basis of available resources, and not on task appropriateness. In the case of simulating the mechanical behaviour of irregular anatomical structures in biomedical engineering, the authenticity of two-dimensional model behaviour and the interpretation of model solutions is of particular concern since little comparable two-dimensional and three-dimensional data have been published. As part of a research programme, a comparison was made between two-dimensional and three-dimensional finite element models (FEMs) that examine the stress-strain environment of a clinical bone fracture and callus. In comparison with the three-dimensional model, the two-dimensional model substantially underestimated peak compressive principal stresses in the callus tissue and peak equivalent strains. This was a consequence of geometrical and structural asymmetry in a plane perpendicular to the two-dimensional model. However, the two-dimensional model predicted similar patterns of stress and strain distribution to the corresponding mid-longitudinal plane of the three-dimensional model, and underestimates of peak stress and strain were much reduced. This confirmed that despite the irregular geometry and structure of the subject, the two-dimensional model provided a valid mechanical simulation in the plane of the fracture that it represented.