Vite Bh ck be teddd de oe at. i
atalalall
60
(m) Measurements of the tracer content of soft
tissue.
microscopic volume of bone in which appositi
Data for Animals
occurring, the apposition rate measured bytetrac,
labeling agrees with the value of 4s; measured fo:
(a) Radioisotope kinetics.
(b) Quantitative autoradiography.
(ce) Ratios of uptake in different bones and parts
of bone.
(d) Tetracycline labeling of dogs, cats, and rabbits.
(e) Whole body retention functions for dogs and
rabbits.
(f) Surface to volume ratios for bone from dogs.
MODEL OF THE SKELETAL METABOLISM OF THE ALKALINE
EARTHS
1. Basie Postulates
Macroscopic—(a) The retention function is either a
modified power function or a sum of many exponential
terms. (Whenavailable, both forms should be quoted.)
(b) The retention function for adult man is prac-
tically independentof the age at injection after age 25*
(age-invariance postulate).
(c) There is no long-term discrimination between
alkaline earth elements in transfers between blood and
bone (postulate of no discrimination). (This postulate
is needed onlyto derive the final exponential from the
early plasma clearance. If one takes a value of \ from
other information, it is not required.)
(d) The rate of excretion of activity from the body
at any time is proportional to its current concentration
in the blood plasma {exeretion postulate).
Microscopic.—(e) Caleium transfer between blood
and bone can be completely described by four processes:
apposition, resorption, augmentation, and diminution.
Apposition and resorption are the osteoblastic and
osteoclastic processes which affect local bone volume.
Augmentation and diminution include all the processes
of calcium transfer which take place in existing bone
in the absence of apposition and resorption.
(f) Diminutionincludes both the calcium transferred
from bone to blood by diffusion (long-term exchange)
and that transferred by Bélanger’s osteolysis. Augmen-
tation includes the calcium transferred from blood to
bone both by diffusion (long-term exchange) and bv
secondary mineralization. The
rate
of
secondary
mineralization in a given volume of bone is its augmentation rate minus its diminution rate.
(g) The total rate of long-term uptake of calcium
in the skeleton, the kinetic A-value or addition rate,
* An onset of osteoporosis of about 1%/year after age 50 is
characteristic of the general population, but this can be simply
superimposed on the predictions of the present model.
tT A-values have long been called accretion rates in the literature, but this is a misnomer.
is equal to the sum of the apposition rate and thi
mentation rate. It is found experimentally that
bone volume bycalcium kinetics. A; refers to the
of 4 at 5 days after injection. Augmentation r.
defined as the value of A; for a volume of bo
which there is no apposition. (See Reference 2
complete development of these observations and<
tions.)
(h) Augmentation rates may depend to som
tent upon the metabolic state of the skeletal syst
a whole—the data on this point are not yet concl
However, the main determinant of the augmen
rate of a given volume of boneis the age of that bx
If the bone has been formed recently (within th
few years), it will have a much higher augment
rate than if it had been formed manyyears ago. °
is, therefore, a distribution of augmentation
throughout a given region of bone which depends
the distribution of local bone ages within that r:
And the distribution of local bone ages depends
the rate of apposition-resorption.
(i) The data obtained so far for the augmen
rate as a function of local bone age in experin
animals and two men“? can be well represented |
expression
Augs = 30f-°7
> 0.2 year,t
where Aug; is the kinetic A-value calculated 5
after tracer injection for bone in which the app
rate is zero (no bone formation taking place), gi
percent per year, and ¢ is the local bone age in
For ages (¢-values) between about 0.2 year and 1
Augs represents mainly secondary mineralizatio:
i-values greater than 1 year, secondary minerali
is largely complete and Augs represents main!
diffusion of calcium into fully caleified bone.
diffusion 7m is balanced by a corresponding r:
diminution or diffusion out. This augmentation-di:
tion continues throughout the life of the bor
normal adult animals and normal man it appe
represent the greater part of the calcium transtf
tween blood and bone.
(j) In a given region of adult human bone, s
the cortex of a long bone, the spatial distribut:
resorption sites is assumed to be random. (One
this postulate to calculate the age distributionol
volumes, given the turnover rate \ and the age
subject.) This assumption of randomness cou
tA complete list of terms and definitions will be fc
the end of this article.