Biomedical Engineering Reference
In-Depth Information
−
1
dt
ε
()
σ
η
Et t
(
−
)
0
=
e
(10)
c
η
dt
From equation (10) is evident, that the strain rate of articular cartilage in interval of
t
∈〈
t
0
; t
1
〉
decelerates. The strain rate shortly after the load is the highest.
2.2.2 The strain rate of articular cartilage in peripheral zone during the strain
relaxation
The strain of peripheral zone in time
t
1
during unloading is given by equation (11):
−
1
Et t
(
−
)
1
ε
()
t
=
ε
e
η
(11)
t
1
dt
ε
()
The strain rate
=
ε
() 0
t
<
. It means that the strain function
ε(t)
in interval of
t
∈〈
t
1
; t
2
〉 is
dt
decreasing. The strain rate in the same interval of 〈
t
1
; t
2
〉 is decreasing also. Strain rate
during the strain relaxation in interval of 〈
t
1
; t
2
〉 is given by equation (12):
dt
ε
()
−
1
−
⎡
E
⎤
Et t
(
)
1
=
ε
e
η
−
η
(12)
⎢
⎥
dt
t
1
⎣
⎦
The strain rate of articular cartilage shortly after the unloading (during the strain relaxation)
dt
dt
ε
()
is distinctly higher than to the end of interval of 〈
t
1
; t
2
〉 . Strain rate
with increasing
time in interval of
t
∈〈
t
1
; t
2
〉 is decreasing.
3. Conclusions
The above described analyses lead to the formulation of the following key conclusions:
Synovial fluid is a viscous pseudoplastic non-Newtonian fluid. Apparent viscosity of SF
decreases with increasing rate of flow velocity gradient. SF does not display a decrease in
viscosity
over time at a constant flow velocity gradient
(as it is typical for thixotropic material).
The rheological properties of synovial fluid essentially affect the biomechanical behaviour of
SF between the opposite AC surfaces and in the peripheral AC zone also. During the shifts
of the femoral and tibial part of AC in opposite directions the velocities of SF flows decrease
in the direction towards the neutral central zone of the gap between the AC surf
aces. Non-
linear abatement in viscosity
in the direction from the
neutral (“quiescent“) layer of
SF
towards the opposite AC surfaces contributes to the lubrication quality and very efficiently
protect the uneven micro-surfaces of AC.
The viscoelastic properties of the peripheral zone of AC and its molecular structure ensure
the regulation of the transport and accumulation of SF between articular plateaus. The
hydrodynamic lubrication biomechanism adapts with high sensitivity to biomechanical
stresses. The viscoelastic properties of AC in the peripheral zone ensure that during cyclic
loading some amount of SF is always retained accumulated between articular plateaus,
which were presupplemented with it in the previous loading cycle. During long-term
harmonic cyclic loading and unloading, the strains stabilize at limit values.
The limit strain value of AC during loading is always greater than its limit strain value after
unloading. Shortly after loading, the strain rate is always greater than before unloading. In
