71
1 Was Sey ventions are pertinent here.“* The data in Table 29
TABLE 29.
Summary OF JoWSEY’s Data ON BONE SURFACE
IN ADULT Human BONE
erles Mode. the average values for normal human bone for
byes 35, 45, 55, and 65 taken from Jowsey’s graphs in
Percent of total bone surface
he above reference. (There appears to be very little
The decatgy..ccular iliac crest, very little error will result from
1, howevethe assumption of equal fractional areas, particularly
or formation.
which thy
‘(he volume turnover rates are, therefore, almost
that thgpraportional to the respective surface-to-volume ratios.
e iteratiyg
‘The right hand column shows the respective turnhe amounfover rutes based on the formation surface from Table 29
neration fard a linear apposition rate of 0.8 n/day. Lee® has
Rib
|
|
Anterior iliac
2.6
3.3
4.6
7.0
2.8
3.9
2.9 + 0.4 (S.D.)
5.2 + 1.6 (8.D.)
crest
Femur midshaft
Avg.
TABLE 30.
Turnover Rates or DIFFERENT Bones Usine
TABLE 29 FOR FORMATION SURFACE
Surface/
cm/cm?
P duit dogs they average 1 »/day. Villanueva et al.9”
frcport a linear apposition rate of 0.8 + 0.3 u/day(8.D.)
the bon
Typical Calculation
= 2.0%%
1; ve use the values for femur midshaft from Jowsey
osonly Llovd and the apposition rate of 0.8 u/day from
ps only
the thirc:
frost:
Resorption
Formation
a
hanwe with age in this age range.)
F \jthough the values are somewhatlarger in the very
Cortical bone
Mid-femur
Trabecular bone
Femur head
Thoracic vertebra
Lumbar vertebra
Rib
Formation
surface, %
Turnover Turnover
O%, /year
ratios
30
2.8
2.5
1
75
90
90
90
2.9)
2,9)
2,.9@
2.6
6.4
7.6
7.6
6.8
2.6
3.0
3.0
2.7
(a) Average value from Table 29.
e percent 2.8‘. (30 em/cm?) (0.8 n/day)(365 days/year)(10~*em/z) = 2.5 %/year (turnover rate of the femur midshaft).
ht reves,
The ratios between these turnover rates in different
valid. Te ones are quite close to those observed in the Sr
Table 28.@Nie surements in man. Apparently the ratio of the
S of the surtiuce-to-volume ratios gives a reasonable estimate of
meee ithe ratio of trabecular-to-cortical turnover. In addicr bonestien, Lloyd’s surface/volume ratios together with
sn Foy Jowsey’s formation surface and Frost’s mean apposiin Option rate lead to acceptable absolute values of the
ir site gturnover rates. It would be most valuable, therefore,
of stress. to huve more measurements of the surface/volume
Tutio in different bones both in dog and in man.
-
Cortica®”
\vle on Linear Resorption Rate
t
Co,
.
=“ Note that if resorption proceeded at the same
0.\ u/day as does apposition, and if theiliac crest had
. & surface/volume ratio of 90 cm/cm?, then Table 29
volume rates of apposition and resorption. Perhaps the
effective linear resorption rate is only about 0.4 u/day.
MATHEMATICAL SUMMARY OF MACROSCOPIC MODEL
1. The whole-bodyretention function is either
Case (a) A power function followed by an exponential
R=
e(t + 6)”
t
beh by bist
(et, eye
t
IIA
(Conclusion
ty
(32)
IV
,
he distri.
(31)
ty
(33)
Case (b) A power function times an exponential
R= e(t + e)e™
(34)
Case (c) A series of exponentials.
2. In any case, the total area under the retention
curve is given by ¢/nk (which follows from the model
of the skeletal metabolism of the alkaline earths,
postulates 1(b), 1(¢), 1(d)). This assumes that the
system is age-invariant with no long-term discrimina-
P&-ts that the high values for resorption surface in
Table 29 do not indicate an imbalance between the
tion between blood and bone.
3. From step 2 it follows that for cases (a) and (b)
in Step L: