Biomedical Engineering Reference
In-Depth Information
t
∫
N
=
f
()
tdt
′
′
(5.3)
R
a
tT
−
R
and
N
F
is found by integrating over the refilling period
tT T
−+
(
)
RI
∫
N
=
f
()
tdt
′
′
(5.4)
F
a
tT TT
−++
(
)
RI
F
Normal values of
T
R
= 24 days,
T
I
= 8 days, and
T
F
= 64 days were calculated
from several histomorphometric studies [1,52,53].
5.3.3 BMU Activation Frequency
In Hazelwood et al. [1], the BMU activation frequency,
f
a
( B M U s/a r e a/t i m e),
was assumed to be a function of disuse as well as of the existing state of
damage. Also, because BMUs must start on a bone surface,
f
a
was taken to
be a function of the internal surface area of the bone region. Specific surface
area (internal surface area per unit volume,
S
A
) was determined from poros-
ity using an empirical relationship [1], normalized to values between 0 and 1.
Allowance was thus made for the greater potential for remodeling offered
by large surface areas within a bone by letting
f
a
= (
f
a
(
disuse
)
+
f
a
(
disuse
)
)
S
A
(5.5)
where
f
a
(
disuse
)
and
f
a
(
damage
)
represent contributions to
f
a
from disuse and
damage, respectively.
5.3.4 Rate of Fatigue Damage Accretion
In their study, Hazelwood et al. defined the damage (D) as total crack length
per section area of a bone. With this definition, they presented the fatigue
damage accretion rate as
R
(5.6)
DD D
F
=−
where
D
F
and
D
R
represent the fatigue damage formation and removal
rates, respectively.
D
F
is assumed to be proportional to the product of the
strain range raised to a power and the loading rate (
R
L
,
cycles per unit time)
summed over
n
discrete loading conditions [47]:
n
∑
q
Dk
=
ε =Φ
Rk
(5.7)
F
D
Li
D
i
i
=
1
