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.