66 BONE SURFACE EXCHANGE The initial deposition of the alkaline earth elements within hours after injection is similar to that of the bone-surface-seekers. Tracer leaving the blood rapidly transfers to all bone surfaces near blood vessels. This phenomenon has recently been investigated by Rowland? using Ca in adult dogs and rabbits. It is important to emphasize the difference between bone surface and bone crystal surface. From in vitro experiments with bone crystals in water one learns that the initial uptake of “Ca in vitro is by exchange with the calcium atoms at the surfaces of bone crystals. However, this is nof an adequate description of what happens in vivo, although it is often so stated in the literature. In vivo, only the bone crystals which lie at bone surfaces take any part in the short-term exchange of calcium. These crystals at bone surfaces constitute only about 0.1% of all the bone erystals m the body. The rest (99.9%) are buried within the organic matrix with very little water so that it takes a considerable time for “Ca to reach them bydiffusion from the blood (fromdaysfor the erystals nearest canaliculi to perhaps years for those furthest removed“), The bone surfaces involved in this early exchange are the endosteal and periosteal surfaces of cortical bone, the walls of haversian and volkmann canals, and the surfaces of trabeculae. Bone surface exchange must, therefore, be earefully evaluated (particularly for isotopes such as “Ra which have a short half-life) because the cells lining bone surfaces appear to be a prime target for osteosarcomainduction. Our information about this component of skeletal metabolism comes from two sources: Rowland’s experiments on dogs and rabbits with Ca, and alkaline earth kinetics for times shortly after injection. Rowland found by quantitative autoradiography and_ blood curve analysis that the amount of calcium involved in the exchange at bone surfaces was equivalent to that which lies within 2000 A of each bonesurface. The same depth was determined for dogs and rabbits. Whether all crystal calcium within 2000 A of each bone surface is involved or only the calcium at erystal surfaces within a depth of 10,000 A (1 micron) of each bone surface cannot be determined from the autoradiographs. However, the total amount of calcium involved is about 0.1% of the bodycalcium (this follows from the figure 2000 A times the surface-to-volume ratio for the human skeleton, 42 em?/cem*, measured by Lloyd). The difference between the exchange in dogs and rabbits is a question of time scale: the exchangeable 45Ca activity reached a maximum in dogs about 15 hr after injection, while that in rabbits reached a maxi- mum about 2 hr after injection. If the modifier function model, R = é(t + 6), is fitted to Ro data for plasmaspecific activity, the value of ¢ rabbits is 1.6 hr and that for the dogs is 12 hr. analysis of the power function model“ showec is equal to £/Ao and hence to the turnover tin initial pool. This relation, together with the corr ence between the value of « and the time of m: exchangeable activity in the dogs and rabbits, that the power function parameter ¢ 1s very | associated with the time of maximum tracer up bone surfaces. We would like more data on th: particularly in man, but it seems reasonable tu ate the best estimates of the e-values for the ; earths in adult man (0.18 day for radium, 0.26 strontium, and 2.5 days for calcium) with the maximum activity at bone surfaces due to excha: Thesize of this initial pool by kinetics of the « earths in dogs and manis about Hy = 0.25%e, ° is body calcium. This is somewhat larger tha: land’s measurement, of the size of the bone surfac The difference is probably due to the fact that the initial pool of caleium is located in soft Heaney“! estimates that 60of the short-te cium pool in man is soft tissue, which fits Ro measurement and the kinetic measurement vel The exact behavior of the heavier alkaline earth: surface exchange is still a matter for con] Ellsasser’s“3? measurements of barium uptake dog indicate that at least up to about a wee injection barrum and radium maybe prefer deposited on bone surfaces by a factor of two c over calcium. This needs further investigation. If we assume that Rowland’s figure of 20( applicable to all the alkaline earths in man, tl can use the area rule [2(a), (b), (¢)] to caleul: dose to bone surfaces due to this short-term exc In a steady state system with no discriminat tween blood and bone, the continuous introduc activity into the blood at a constant rate woul produce equality between the specific activi. plasma and the caleium in the exchangeable bone surfaces. Therefore, after a single injecti time integral of the plasma specific activity S a pool specifie activity V from the time of inject timeinfinity are equal: [ vat= | Sat = q/nk, 0 0 in which the third quantity, ¢/nk, follows from « sion (19). The dose accumulated at the bone - due to this exchangeable activity is then direc lated to the number of microcurie-days per em” o oe