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
 
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