Biomedical Engineering Reference
In-Depth Information
However, Rubin, Xu, and Judex [62] demonstrated that loading at frequencies
up to 90 Hz can still have an effect on bone formation. A logarithmic func-
tion is used to describe the relationship between frequency (
f
) and osteocyte
mechanosensitivity (
MS
OST
):
MS
OST
∝ ln(
f
+ 0.5),
MS
OST
≥ 0
(7.35)
Data from Burr, Robling, and Turner [63] show that osteocyte sensitivity to
mechanical loading is proportional to 1/(
N
+ 1):
1
MS
∝
( 7. 3 6 )
OST
N
+
1
This means that bone loses more than 95% of its mechanosensitivity after
only 20 loading cycles. It can be imagined that osteocytes will regain their
sensitivity after a period of rest between loading bouts. Robling, Burr, and
Turner [57] demonstrated the following relationship:
(
∝−
−
)
T
rest
τ
MS
2
e
( 7. 3 7 )
OST
where τ is a time constant equal approximately to 6 h [57]. It is noted that 98%
of bone mechanosensitivity is regained after 24 h of rest.
Bone cells accommodate to routine loading, which means that bone mech-
anosensitivity drops as the loading period extends [58]. Qin and Wang [2]
hypothesized that bone mechanosensitivity follows the relationship with
loading period
t
(days):
∝
−
tT
acc
MS
e
( 7. 3 8)
OST
where
T
acc
is the time constant describing the rate at which accommodation
takes place—here assumed to be 24 days. Making use of Equations (7.35)-
(7.38), osteocyte mechanosensitivity can be written as
(
)
ln
f
N
+
+
0.5
1
(
)
−
T
τ
−
t T
MS
=⋅
K
⋅ − ⋅
2
e
e
acc
( 7. 3 9)
rest
OST
S
where
K
MS
is a proportionality constant.
In most animal experiments, the mechanical stimulation is applied for no
more than 1 h per day and lasts for several months [12,64]. The conclusions
from animal studies are that limited benefit is derived from additional load-
ing cycles above approximately 40 cycles per day [6], and it has been clear that
NO and PGE
2
production appear within minutes [44] when the mechanical
loading starts, ending several hours after the loading stops [65]. In this chapter,
a short time scale is used to describe NO and PGE
2
production caused by a
mechanical stimulus, which is assumed to be much faster than changes in the
