g 69 SKELETAL DISCRIMINATION BETWEEN SR AND CA TABLE 2. Comparative calcium and strontium parameters Compartment Sizes. g subj — Isotope T I 2 ! | 1 Transfer Constants, g/d | ——— Ca Sr) : 2 2.40 .38 2.304 .25 : Feces pp Accretion py pai, it 2.30cb 137 224s 27 4-70 .24 4-54cb 16 .072-b .004 .280+ .011 .230-+ .014 .250-+ .O1i -350+ .036 .358+ .026 1 .89+ .30 1.g2 .23 2.50.75 2013.31 3-884 .19 3.06.7 ob42b .006 | . 180+ .065 .o88+ .o11 102+ .037 330+ .033 .262-+ .083 4-351.31 4.07+6.08 1-79-34 3.73.71 | ! 3-50e.18 6.49.39 | | 186.015 .607.041 -176+ .016 659 .043 474+ .062 3372 .067 2.12+.40 2.27.43 ' : 3 Ca Sr 1.71.29 ! 2.704 .57 4 Ca Sr | | 2.074 .31 1.g2+.17 3.524 .39 1.87.14 | 5.50.17 3.79.10 . 129.006 -349-b .O10 -149-b .012 .216 .007 4342 .056 172+ .023 2.18+.24 1.22 .0g 5 Ca Sr | | 2.28 .27 2.042 34 5-01.30 2 392k .35 | | 7294.15 4-43.18 .061 + .002 -131 + .006 1474 .007 .090-k .005 .428-+ .059 .44. .038 2.26.14 U.54.23 8 Ca Sr | 2.761.392 2.58+ .32 1.851.465 3.752 .62 | . 4-61.69 6.334 .34 | .015-+.002 -12Q- .007 -173+.026 .245 .013 .3970+.067 349+ .034 3-9043.11 3.82 .63 Lo Ca | 1.47.32 2.114.53 | 3.58.14 | .050- .004 . 108 .009 194+ .O1g -172+ .026 .2214 .027 3.17.79 .065+ .017 +242 .057 -146- .017 .208 + .052 353 .034 . 289 .041 2.51.30 2.18.98 | | Urine pa Ga Sr Sr: 1.38 .yo 1.0521 .19 r+ 2 | | 1.10.55 1.971 .23 3-074 .25 | 4-752 .52 4-61 .52 | | Kt oy, Ca Sr | : t.gg4t.t7 2.072 .22 | 2,814.45 2.542b .30 | | -172c .025 |: 3.30+2.01 Values are means + standard deviation of value (o,). ¥ = mean, ¢,, = standard error of sample. Compartment 1 = plasma extracellular, intracellular Ca space; compartment 2 = exchangeable bone. p3: = accretion—flow into bone, pa = urinary Ca ex. cretion, py = fecal (endogenous) Ca excretion, px = flow into exchangeable bone, p12 = flow from exchangeable bone into compartment 1. the experiment; 2) the rates of transfer of the substance being traced, between compartments, and into and out of the system, are constant during the experiment; 3) intracompartmental mixingis rapid. Thesolution of the equations describing the linear twocompartment open model (shown in Fig. 1) gives parameter values which fit the observed data and therefore the model appears to be consistent with the data, Compartment 1 is assumed to consist of plasma-extracellular space and intracellular space of soft tissue and possibly some exchangeable bone. Since compartment 1 achieves equilibrium in 30 min, the above-mentioned sub- compartments are lumped together in the model. Coimpartinent 2 comes into equilibrium within 2-3 days and is assuined to consist largely of rapidly exchanging bone. Activity is transferred from compartment 1 to compartment 2 (pn) and is lost to ‘‘slowly exchanging” bone (p31), and to the outside via urinary excretion (p.,) and endogenous fecal excretion (;;). Although in the model the slowly exchanging bone (compartment 3) is illustrated as feeding back (3) into compartment1, in the short-term study (10 days) described here, compartment 3 is treated as an irreversible open compartment similar to the urine and feces compartments (p13; = 0). The tracer is presumed to move slowly through this compartmentuntil it reaches the resorption sites in significant quantity. Thus the 10-day data were insufficient to derive this feedback function for either Ca or Sr. Thus compartment 3 1s illustrated in Fig. 1 as a series of subcompartments or as SUEZ (U4 an infinitely expanding compartment. Longer term data are required to obtain the resorption or slow-exchange rate from bone. Computer analysis. The solution of the model parameters, i.e., Compartment sizes and transfer constants, was per- formed on an IBM-7094 with the NIH-OMR SAAM program (2-4). Once the initial estimates are provided, the program solves the required differential equations by an iterative procedure. The program computes set of values for the parameters that give the best least-squares fit of the data to the model. The least-squares solution gives values of the parameters and their standard deviations as well. Since only the plasma data are expressed in absolute values, it is necessary to determine a proportionality constant (k) for each set of data. The computa- tion of these constants (k) is also included in the computer solution. In the computer solution, the whole-body counter data and the knee data are handled by a summer. The summer develops a linear combination of the data of the various compartments to fit the whole-body and knee data. In the summation of the whole-body counterdata, the three compartments were weighted equally by a fixed factor, designated sigma. In analysis of the knee data, the sigmas for each compartment were independent and determined by the computer. A more detailed ex- planation of this aspect of the computer program was presented in an earlier study (unpublished data). map rege Tee ARATE pTaang EE of the substances being traced remain constant during