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

lengthening, respectively, if compared to their full extension lengths.
The maximum forces experienced by lateral and medial collateral ligaments were 230 N
and 170 N, respectively (Fig. 4).
Figure 4 - Ligament force pattern: data extracted when a steady-state condition was achieved.
3.3 Tibio-femoral contact forces
Our numerical simulations showed that TF contact forces increased with flexion in a
non-linear way; a gradual growth in the early stages was followed by a sharp increase,
up to a value of 4.58 BW, in the angle range between 60° and 90° of flexion.
DISCUSSION
Force [N]
450
400
350
300
250
200
150
100
50
0
Ligament Force
0 10 20 30 40 50 60 70 80 90
Flexion angle [deg]
Although the results of our multibody musculoskeletal model have been obtained in a
‘quasi-static’ condition, the model itself includes the dynamic properties of rigid bodies,
and allows to compute the final position achieved as a result of the applied forces and
constraints. Starting from an initial, unbalanced condition, the model is led to adjust its
ligament lengths, muscle force, and bone relative positions in order to sustain the load at
a predefined knee joint angle. No kinematic constraints are applied to the knee, except
the prevention of interpenetration between femoral and tibial surfaces.
Our results have a good similarity with data already presented in literature. Quadriceps
muscle force is in agreement with the pattern identified by Innocenti et al., (2011), and
Sharma et al., (2008). At 90° of flexion we obtained a force value of 3.88 BW. By
considering that our vertical load at the hip was 300 N (50% more than the load applied
by the above authors) our results are very similar to theirs (2.7-2.9 BW).
Ligament length patterns are consistent with the ones reported by Bergamini et al.,
(2011). Particularly, the ACL trend presents a peak at 15° of flexion and a decrease of
21% of the full extension length at 90°, in agreement with literature data [9]. Our
preliminary results show a 10.5% shortening for the LCL and a 5% lengthening for the
MCL: these findings are consistent with those of Bergamini et al., (2011), who reported
11% and 3%, respectively.
TF contact forces are very high during a squat movement. Previous studies [4,10] have
obtained a range from 3.73 BW to 6.2 BW. Our results are within this range of values.
As a reference, Innocenti et al., (2011), reported an average contact force between 3.2
BW and 3.7 BW at 90° of flexion; by considering the higher vertical load we applied,
ACL
PCL
LCL
MCL