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

With the following boundary conditions:
zz(0, t) PA ( t)
(2)
u( h, t) 0
(3)
Where zz(z,t) is the axial partial stress of the solid matrix, k is the strain-dependent
intrinsic permeability and PA is the contact pressure applied on articular cartilage
surface. The contact pressure was obtained by dividing the normal contact force by the
tibio-femoral contact area. This contact area is known to vary as a function of knee joint
angle [11]. Surface displacement was found by solving Eq. (1). Simulating cartilage
displacement during gait starting from rest (i.e. zero initial conditions) is not a realistic
condition. Therefore, for each subject, a constant load equivalent to one body weight
was first simulated during 15 minutes prior to the simulation performed with contact
loads during gait. The amplitude of this preloading represents the tibio-femoral contact
load of a person standing up. Time increment (t) and space increment (z) were set to
0.025 s and 0.25·h respectively during the preloading simulation and to 1/120 s and
0.25·h respectively during the gait simulation. Material properties used in this study
were taken from literature. Surface friction force () was estimated from this equation:
( t) ( t) F ( t)
(4)
eff contact
Where eff is the efficient friction coefficient and Fcontact is the normal (compressive)
contact force. The efficient friction coefficient was defined as:
s
2 pt ()
eff ( t)
eq 11 (5)
PA() t
Where s is the solid content, p(t) is the interstitial fluid pressure, and eq is the
equilibrium friction coefficient. Solid content was assumed to be 0.2 and 0.15
respectively for healthy articular cartilage and OA articular cartilage. The equilibrium
friction coefficient was taken from Bell et al. [12] for dynamic loadings and were set
respectively to 0.03 and 0.075 for healthy and OA articular cartilage. Interstitial fluid
pressure was obtained by solving momentum equation for the fluid phase which gives:
f
h
f
p() t s
v z, t v z, tdz
(6)
0 k
Where v s and v f are respectively the velocity of the solid phase and the fluid phase. The
velocity of the solid phase was obtained by taking the derivative of the articular
cartilage displacement with respect to spatial coordinate and the velocity of the fluid
phase was obtained by solving the continuity equation:
f f
s s v z, t v z, t
0
(7)
Where denotes the spatial gradient. Results for each subject for the surface friction
force, the normal contact force applied, and the friction coefficient were resampled and
then averaged over one gait cycle. Statistical ANOVA analysis was performed to
determine whether significant differences exist between healthy and OA articular
cartilage for the normal contact force applied the friction coefficient and the surface
friction force.