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

THE INFLUENCE OF UNCERTAIN ANATOMICAL PARAMETERS ON
THE RESPONSE OF FINITE ELEMENT MODELS OF THE HUMAN
LUMBAR SPINE
1. ABSTRACT
F. Niemeyer 1 , H. J. Wilke 1 and H. Schmidt 2
Contemporary finite element models of the human spine contain a vast amount of highly
uncertain independent parameters. A systematic exploration of the impact of interindividual
variability in geometry on the biomechanics of the spine is still pending. To
address the question, whether deterministic models suffice to represent the biomechanics
of the human lumbar spine, we analyzed the effects of randomly distributed geometry
parameters on the distribution of different model responses.
2. INTRODUCTION
Finite element (FE) models of the human spine (or parts thereof) are in wide use today
to investigate the biomechanics of the healthy spine and the effects of various kinds of
degeneration processes. Numerical simulations have also proven valuable for comparing
the performance of different implants.
The usual way of creating such models based on a single CT data set yields a model that
represents one single and hence highly specific anatomy. Yet, we know that the spine’s
anatomy can indeed vary widely between different persons—which begs the question,
whether it is valid to use such models to deduce generalized statements about the human
spine. Can a deterministic model based on a single specific geometry really represent
the biomechanics of a broad range of anatomically different spines? Or should the geometry
of FE models reflect this inherent inter-individual variability?
Answering these questions requires modeling uncertainty itself, a method long known in
engineering under the name of probabilistic design. In our case, we used this method to
estimate the influence of the uncertainty in geometry parameters on the biomechanical
behavior of an L3-L4 segment. Note that the variability in the parameters can be due to
both inter-individual anatomical variability and measuring errors.
4. FE MODEL OF THE L3-L4 SEGMENT
To enable automatic generation of an arbitrary amount of model variations and to keep
the computational cost bearable, our FE model abstracts from minor anatomical details
quite heavily and only models major geometry features (Fig. 1). For modeling the disc
and ligaments we use an approach analogous to that described by Schmidt et al., 1,2 using
uniaxial reinforcement elements with non-linear tensile stress-strain behavior. We apply
1 Institute for Orthopaedic Research and Biomechanics, Ulm University, Ulm, Germany
2 Julius Wolff Institute for Biomechanics and Musculoskeletal Regeneration, Charité, Berlin, Germany