ever, if the actual stress magnitude exceeds the ideal
value, the elastic deformation also increases. This has
‘he effect of a stimulus on the bone cells in that the
ouild=-up now predominates. Thus, the supporting crosssection
 of the bone is enlarged and given uniform force,
the stress must decrease accordingly. This in turn means
that the stress magnitude will fall short of the ideal
value which leads to a decrease in elastic deformation
thus encouraging the decomposition of bony tissue;
the bone is subject to atrophy and its supporting crosssection
 decreases in size. This means that the stress
will increase so that the build-up of bony tissue once
again takes precedence. Thus, in this fashion the
quantity of bony tissue must vary between alternating
ouild=up and decomposition in such a way that the
ideal magnitude of stresses is reached and the skeletal
element thus attains flow equilibrium.

Qualitively, this process can be most closely approximated
 with a third degree mathematical function. It
depicts the dependence of the actual reconstruction rate
U on the stress magnitude &, A positive sign for U
indicates predominance of bone build-up, a negative
sign indicates the predominance of decomposition. From
the curve shown in Fig.15, one can see that belowa
certain stress magnitude, 6, there is no further bone
decomposition; rather the build-up and decomposition
of bony tissue once again reaches equilibrium. This
fact has been documented by observations by Bairati
and colleagues who, observing totally non-strained rear
extremities in dogs, noted that there is a severe re~
duction in bone tissue but no complete dissolution of
the skeletal elements. With increasing 6, a flow
equilibrium will finally be reached at the ideal value
of 8%; further increase in & will effect a predominance
of build=up (+U) while at an upper limiting value 65
bone build-up will suddenly revert to bone decomposition.
 This does not mean a direct mechanical
destruction of the bone = as in injury = but rather a
slow disappearance of bone due to the increased
activity of decomposing osteoclasts.
Figure 14
done as a cybernetic system (from Kummer 1963).

Figure 15
Mathematical approximation of the presentation of the
dauwelsian "structural law" of bone (from Kummer
1963).

FORCE

STRESS

2
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DD

LASER

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3ild 14
Der Knochen als Regler (aus Kummer 1963).
Bild 15
Mathematische Näherung zur Darstellung
des PAUWELSschen "Baugesetzes" des
Knochens (aus KUMMER 19463) .

972