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

curve for each sensor which varied over time corresponding to the loading and
unloading of the femoral component. A custom program was developed in LabView
that extracted the amplitude of each sensor’s displacement curve at 1 cycle intervals
over the whole 40 cycles, this gave the values of inducible displacement due to loading
for each sensor over the test period.
Coordinate transformation theory for small angles [8] was then applied to allow the
displacements (u, v, w) and rotations (θx, θy, θz) of the femoral component relative to
the bone (or micromotions) to be determined for a fixed reference point (Fig. 1). If Uc,
Vc and Wc are the displacements measured by DVRT 2, DVRT 1 and DVRT 3
respectively; Va and Wa are the displacements measured by DVRT 6 and DVRT 5
respectively; and Wb is the displacement measured by DVRT 4 then it can be shown that
⎛U
⎜
⎜Va
⎜
⎝W
a
a
U
V
b
W
b
b
Sensor input
matrix
The terms Ax, Ay, By, Cx, Cy represent the distance each target sphere is offset from the
reference point as shown in Fig. 1c. Equation 1 can be simplified to give the required
translational micromotions (u, v, w) and rotational micromotions (θx, θy, θz).
4. RESULT
Uc
⎞ ⎛1
⎟ ⎜
Vc
⎟ = ⎜θz
W ⎟ ⎜
c ⎠ ⎝−θ
y
−θ
1
θ
x
z
θy
⎞ ⎛ Ax
⎟ ⎜
−θx
⎟×
⎜ Ay
1
⎟ ⎜
⎠ ⎝0
Rotational matrix Offset matrix
(Fig. 1c)
0
B
0
y
Cx
⎞ ⎛u
⎟ ⎜
Cy
⎟ + ⎜v
⎟ ⎜
0 ⎠ ⎝w
u ⎞ ⎛ Ax
⎟ ⎜
v ⎟ −⎜
Ay
w⎟
⎜
⎠ ⎝0
Mean translational and rotational micromotions for the cases considered are shown in
Fig. 2. It can be observed that all translational micromotions generally increase with
flexion angle. If we examine the individual components of motion we can see that the
largest translational micromotions occurred in the z direction (distal/proximal). For the
flexion angles tested the z direction component of loading was the largest. Figure 2b
shows that the addition of a short stem for both cemented and uncemented cases leads to
a reduction in micromotions in comparison to implants with no stem (PS). The TS
implant with long stem (Fig. 2c) shows significantly reduced micromotions in
comparison to the other two implants. The translational micromotions reduce with
cementing as expected in almost all cases. The trends with respect to rotations are
considerably more complex. In general the largest rotations are found to occur with the
uncemented PS implant. For long stem cases the rotational micromotions can be seen to
be extremely small in comparison to the other two implants. Cementing is found to
reduce rotational micromotions. The component of rotational micromotion found to be
the smallest in general was θz (i.e rotation in the transverse plane).
u
v
w
Transformation
matrix
0
B
0
y
Cx
⎞
⎟
Cy
⎟
⎟
0 ⎠
Offset matrix
(Fig. 1c)
(1)