59 ‘EE Trang fformation. It represents an extension of the power function model and takes explicitly into account the microscopic mecha- in one kind of bone is random as to location, it then specifies the distribution of local bone ages within that ivision Ant7 L-7060, pp, in; RODUCTION rate versus local bone age derived from numerous experiments in animals and man, it calculates the of Complex? pi-ms of tracer deposition and removal. 3. Argonne? on meh In order to calculate the radiation dose to various ironmental? parts of bone tissue from internally deposited radio- e National? nuclides, one needs to knowtheir pattern of uptake and data nnual Re-z «tention within the skeletal system. Appropriate the of estimates existing that so .rn 0878b tn man are scarce, assumpthe been. basedeither on Modernt doses within: bone have on Modern on . . : 1968, Ed:f tion of a uniform distribution of the radionuclide or on 1969), pp.f an observed ratio which relates the activity in newly- _# formed bone to the specific activity of the diet. It is ‘otometrie# 41. purpose of this report to go more deeply into the ; Arsenazof subject and to see whether our accumulating knowledge orium ange of the mechanisms of skeletal metabolism and the . Acta 10, retention of radionuclides can be put to use in the construction of a quantitative bone model. Ne renon The primary interest will be in the bone-volumeLois State iseckers, the alkaline earth radioisotopes of calcium, $ strontium, barium, and radium, because they are most ccurrence f cloxely related to the metabolism of bone itself. The Bull. Int.f pattern of uptake of the bone-surface-seekers, the rare i oactivity eurths and actinides, can probably be related to that t: Uptake € of the alkaline earths through the surface/volume Argonne } ratios of bone. Division A Glossary of terms appears at the end of this report. 30. ANL-F An analysis of the pertinent measurements in bone will F appear in a fortheoming publication. ® A short deserip. . . . | Phvsieg tion of metabolic mechanisms and their possible rela- Well Wa-£ .. une 1959, tlon to osteosarcomainduction are givenin Reference3. vaturally Abstract of Model .Snyder.— Data bearing directly on the dose rate distribution 07sotopes f Minne-§ iris, W., ical Sur11, 234- within human bone as a function of time are scarce. Therefore, our approachis to construct a model of bone remodeling which is flexible enough to fit existing data and yet not so complicated that its parameters cannot be independently compared with experiment. The model ix :un extension of the modified power function model and encompasses the microscopic mechanisms and the + doxe distribution within bone. l‘or the present, the model is limited to the descrip, tion of adult human bone. It considers the skeleton to , be made up of essentially two kinds of bone, cortical bone and trabecular bone. To each kind of bone it ; assigns a turnover rate or apposition-resorption rate. sof huef This determines the amount of tracer activity in the ne have pe inti. . “bution. & Ui! ¢use hotspots. The turnover rate of cortical bone cortical ‘tse determines the time constant of the final exponen- surfaces. tl in the overall retention function. Under the asorganize & “Wnption that this remodeling by apposition-resorption such in- & kind of bone. Using an expression for augmentation distribution of augmentation rates and the overall augmentation rate for each kind of bone. This determinesthe distribution of activity not connected with apposition. The apposition rate and the augmentation rate for each kind of bone are then added to give the kinetie A-value or addition rate, which can be directly com- pared with measurements of total tracer uptake in human bone. The power function or multi-exponential part of the whole-body retention curve is associated with the process of diminution in both hotspots and the diffuse component. The final exponential term in the retention function, which is characteristic of ageinvariant systems, is associated (as mentioned above) with the resorption rate in cortical bone. The model is somewhat overdetermined, which means that internal consistency is obtained only for certain sets of input parameters. Fortunately, these appear to include the best estimates of the actual values of the various parameters from direct measurements. SUMMARY OF BACKGROUND INFORMATION Data for Man (a) The concentration of Sr in different parts of bone as a result of fallout. (b) Radioisotope kineties in man using “Ca, Ca, SSr, Ba,Ra and “6Ra. (c) Quantitative autoradiographyof “*Ra and Ca. (d) The concentration of “*Ra in different bones relative to that in the whole skeleton from autopsies and exhumations of radium patients. (e) Tetracycline labeling of human bone followed by ultraviolet microscopic analysis of biopsy or autopsy material. (f) Microradiographic analysis of formation and resorption surface. (g) Whole-body counting or radioisotope retention over long periods of time. (h) Histological survey of normal bone for resorption surfaces and osteoid seams, (i) Surface-to-volumeratios of cortical and trabecular bone in different locations. (j) Measurements of the amount of trabecular and cortical bone in different locations. (k) Measurements of the composition of trabecular and cortical bone. (1) Ratio of **Ra/”Ra in normal human bone, cortical and trabecular.