Biomedical Engineering Reference
In-Depth Information
represents the other extreme, wherein only minor changes of bone volume
occur during the entire range of parameter variation. These three types of
response curve were excluded from further analysis because they did not
provide an effective control mechanism for bone volume.
In Pivonka et al. [25], the “idealized” regulatory response by functionally
active BMUs is discussed. As mentioned previously, the bone remodeling sys-
tem starts from a steady state, in which it can be identified that Δ
BV
= 0, and
concentrations of various hormones and growth factors cause initial values
of differentiation and apoptosis rates in BMUs. In order to respond to minor
changes in concentrations, it is expected that BMUs should be rather insensi-
tive to these fluctuations. Referring to Figure 7.7, point
A
can be identified as
the concentration threshold, which means that any change in a model param-
eter less than
A
causes no change in bone volume. Further, a region around the
usual operational status of BMUs should be found with relatively small gradi-
ents of changes in bone volume in response to changes in differentiation rates
(regions C-D and D-E in Figure 7.7), and a region with larger gradients for
larger changes in differentiation rates (region E-F in Figure 7.7). It is expected
that this response in bone volume change will remain limited if the differ-
entiation rates increase significantly (the region beyond point F in Figure 7.7)
because an unlimited rise in bone volume is not physiologically realistic.
Conversely, it is expected that the rate of bone volume change will also
decrease in a limited manner if the differentiation rates decrease signifi-
cantly. In fact, it is physiologically reasonable for the bone volume change to
be zero for extremely small differentiation rates. It can also be observed from
Figure 7.7 that point F marks the maximum change in bone volume (ΔB
max
).
Since point A is the maximum concentration that does not lead to further
modification of bone volume, there must be a transition region from point
C to A, which is characterized by point B, the lowest value of bone volume.
Having detailed a potential “ideal response curve,” the search for response
curves that might meet these requirements can now begin. Encouragingly,
a small number of curves are identified that bear similarity to the ideal
response curve. Table 8.1 summarizes all the parameter combinations that
produce idealized response curves. In Figure 8.7, the physiologically realistic
response curve is plotted, which corresponds to the parameter permutation
involving three parameters (
A
OBA
, A
OCA
, A
OST
= -/+/+) and is similar to the
ideal response curve shown in Figure 7.7.
8.5 Effects of PEMF on Patients Undergoing Hip Revision
In the previous sections of this chapter, theoretical and numerical analyses
due to the presence of electromagnetic field were discussed. In this section,
clinical applications of electromagnetic fields in bone healing are briefly
