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: