Biomedical Engineering Reference
In-Depth Information
in Equation (5.2) was determined by setting the area of bone formed to
A
[0.5 + 0.5 (Φ/Φ
0
)] to account for reduced refilling on bone surfaces in disuse
states.
5.3.6 BMU Activation Frequency Response to Disuse and Damage
The relationships between the BMU activation frequency (
f
a
) and both dis-
use and damage were assumed to be sigmoidal, similar to responses found
in pharmacological applications [1]. The coefficients in these functions were
selected to fit the curves within known experimental data ranges. For disuse,
Hazelwood et al. assumed that
f
e
a
(max)
(
f
=
for
Φ<Φ
(5.10)
adisuse
(
)
0
k
Φ−
k
)
1
+
B
C
where
f
a
(max)
is the maximum activation frequency and
k
B
(= 6.5 × 10
10
cpd
−1
)
and
k
C
(= 9.4 × 10
−11
cpd = Φ
0
/2) are coefficients that define the slope and the
inflection point of the curve, respectively.
The relationship between the BMU activation frequency and damage (
D
)
was given [1] as
ff
aa
0(max)
f
=
−−
(5.11)
adamage
(
)
kf
(
DD
−
)/
D
f
(
f
f
)
e
Ra
(max)
0
0
a
0
a
0
a
(max)
where
D
0
is the initial equilibrium damage and
k
R
= -1.6 defines the shape of the
curve. The nominal value for the maximum activation frequency,
f
a
(max)
= 0.50
B M U/m m
2
/day, used in Hazelwood et al. [1] was intentionally chosen to be
higher than the highest average activation frequency (0.14 BMU/mm
2
/d a y).
5.4 A Model for Electromagnetic Bone Remodeling
Based on the hypothesis described in Section 5.3, Qu et al. [2] developed a
theoretical model for calculating the number of osteoclasts,
N
R
,
and evaluating
the corresponding remodeling behavior under electromagnetic loading. This
section provides a description of the developments presented by these authors.
5.4.1 A Constitutive Model
First,
N
R
in Equation (5.3) is redefined by adding an additional term
N
0
as:
t
∫
0
Nf
=
()
tdtN
′
′ +
(5.12)
R
a
R
0