ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

There is no optimal density-elasticity relationship for subject-specific
finite element analyses of human long bones
S. Eberle 1 , M. Göttlinger 2 and P. Augat 3
1. ABSTRACT
Subject-specific FE models of human long bones have to be highly reliable and predict
mechanical parameters with great accuracy to be applicable in a clinical setting. One of
the main aspects in subject-specific FE models of bones regarding accuracy is the
modeling of the material inhomogeneity. The goal of this study was therefore to develop
FE models of human femurs and investigate if there is an optimal density-elasticity
relationship, when the task is to predict the bone’s mechanical response to load. To this
aim, 23 human cadaver femurs were tested in axial compression with a load of 1000 N.
Strains, local displacements, and the axial bone stiffness were determined. Subjectspecific
FE models were developed for each bone based on quantitative CT-scans.
Three different density-elasticity relationships were retrieved from the literature, and
were implemented in the FE models. The predicted mechanical values depended largely
on the used equation. The most optimal relationship was specimen-specific and
depended on bone quality. The most reasonable equation showed a mean error of -11 %
in strain prediction, a mean error of -23 % in local displacement prediction, and a mean
error of +23 % in axial stiffness prediction. The scatter of the predictions was very low
in all three categories of measurements with a 1.96 standard deviation of about 30 % to
the mean errors. This study showed that there is not one optimal density-elasticity
relationship for subject-specific FE models. However, the most reasonable equation
consistently predicted the mechanical behavior of femurs with good accuracy.
2. INTRODUCTION
One of the main aspects in subject-specific FE-models of bones is the modeling of the
inhomogeneous material properties based on quantitative computed tomography (qCT)
(1). The elastic properties are calculated from qCT data by mathematical relationships
between bone density and mechanical properties (2). The density-elasticity relationships
are generally determined by mechanical tests on bone specimens, e.g. (3, 4). Other
studies used an inverse computational approach to determine a relationship between
bone density and mechanical properties (5–8). However, it is still unclear which
density-elasticity relationship results in the highest accuracy, when the task is to predict
the bone’s mechanical behavior. The goal of this study was to develop a verified and
validated framework for subject-specific FE-modeling. It was specifically asked, if there
is an appropriate density-elasticity relationship for subject-specific finite element
models of human femurs, when the task is to predict the bone’s mechanical response to
load.
1 Senior Researcher, Institute of Biomechanics, Trauma Center Murnau, Murnau, Germany
2 PhD-Student, Institute of Biomechanics, Trauma Center Murnau, Murnau, Germany
3 Professor, Institute of Biomechanics, Trauma Center Murnau, Murnau, Germany