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

A Cartesian axis system was defined for each vertebra. In accordance to Stokes’s
(ISO2631) conventional recommendation [6], the origin ‘Oi’ is set up at the centroid of
the vertebral body and the local ‘zi’ axis passes through the geometric centers of the
upper and lower end plates (index i ranges from one to five). In this study, the local ‘xi’
axis was built to pass throw the origin ‘Oi’ and the barycenter of the spinous process ‘Si’
of the defined vertebra (Figure 3). The local ‘y’ axis results from the cross product of
the two other axes: ‘zi’ and ‘xi’.
Figure 3 Internal (O i) and external (E i) references of the lumbar spine used for
the estimation of internal and external curvatures
In this study, the choice of the local ‘xi’ axis allows the estimation of the external
position of the correspondent vertebra. In fact, the intersection point of the ‘xi’ axis and
the low back surface correspond to the external position ‘Ei’ of the vertebra which could
be estimated through the conventional palpation method (Figure 3).
The definition of ‘Ei’ is performed using the property of the cross product as follow:
E [low back surface] which verify this equation:
find i
3.3 Data analysis
OiSi EiS i = 0
Eq.1
Once the positions of the internal (Oi) and external (Ei) references of the lumbar spine
were defined, a MatLab routine was developed to estimate internal and external radius
of curvatures. This method is based on least-squares fit of circle to a set of defined
points (Oi or Ei). Therefore, the prediction of the internal radius of curvature using
external information during three postures was studied. To estimate the robustness of
the prediction model, a change of the ‘Ei’ positions on the cephaladocaudal axis,
through the spinous line were simulated. The magnitude of the perturbation is equal to
+0.03 m. This magnitude corresponds to the relative movement between low back skin
surface and the underlying bone during maximal flexion.
4. RESULTS AND DISCUSSION
S 5
O 5 O 4 O 3
E 5
S 4
E 4
S 3
E 4
S 2
E 2
High correlation values were observed between external and internal curvature of the
lumbar spine (Figure 4). Thus, the use of external lumbar curvature for the estimation of
O 2
S 1
E 1
O 1