COHN ET AL. 68 TABLE 1. Clinical description of experimental subjects Age. yr Weight. kg 48.5 52.7 Mild pulmonary emphysema; old MI Right hemiparesis, partial (CVA); ambu- ‘4 79 6g .t AsHD, mild, compensated 4 69 q4-5 ASHD, mild, compensated 5 63 50.4 AsHD, mild, compensated 8 53 go.4 Idiopathic epilepsy, seizure-free 10 77 67.7 Minimal right hemiparesis, fully ambula- 1 2 80 76 Significant Lesions Abnormal Laboratory Findings Other Pertinent Data Slight increased urinary ? Mild Paget’s disease, pelvis only ? Paget’s disease, right latory PO,” Weakly reactive treated ilium Substernal thyroid) STS; goiter (eu- Minimal osteoporosis tory, -\sHD, minimal, compensated MI = myocardial infarct, CV.\ = cerebrovascular accident, ASHD = arteriosclerotic heart disease, STS = serological test for syphilis. “ee Subj The plasma concentration ofthe isotopes was measured at o.5 and 4 hr andatdaily intervals for 10 days. Plasina samples were counted in a Nal well-type detector connected to a 4o0-channel pulse-height analyzer. Both Ca¥ and Sr*®* concentrations are expressed per 10 liters of plasma (1 g Ca). The whole-body retention of Ca‘? and Sr*® was measured initially at 4 hr after administration (100° _ administered dose) and then at daily intervals in the | A 4 Brookhaven whole-body counter (7). In addition, the | concentration of these tracers in both knees was measured 9 FIG. 1. Compartmental model of calcium kinetics, Compartments are designated as follows: 1, physiological pool of calcium in isotopic equilibrium within 1 hr (plasma-extracellular-intracellular); 2, physiological pool of calcium in isotopic equilibrium within 3 days (exchangeable bone); 3, calcium in “deep bone” or very slowly exchanging bone. The transfer constants, p, are designated as follows: p14 = calcium intake rate, pj = Ca flow rate into compartment 1 from exchangeable bone, ps; = Ca flow rate into exchangeable bone from compartment 1, p13; = rate of resorption and slow exchange from bone, p3, = rate of accretion into bone, py = urinary calcium excretion rate, Bp = fecal calcium excretion rate. 3 — [35 “(y f prior to the study. The subjects were in good health and ambulatory. They were admitted to the metabolic ward of the hospital, but allowed complete freedom of inoverment. A brief clinical description of these subjects is presented in Table 1. at the same intervals, with a 3-inch collimated Nal detector. It was found advantageousto process the large amount of data collected in this study automatically. The output _ of the analyzer was recorded on paper punch tape and _ later transferred to magnetic tape for the IBM-7094. The gamma spectral data were analyzed manually initially, but later in the study the spectral stripping was performed by a computer. Compartment model. The mathematical bases of compart- *. ment theory and its application to biological systems + analysis have been extensively reviewed (10, 13). The kinetics involved in a multicompartment model can be briefly expressed by the followingset of first-order linear , differential equations: A@ = > hig f(t) Diet. Subjects were placed on a constant diet of 800 mg/day of Ca and 1,220 mg/day of P, before and during the study. Blood chemistry. Plasma Ca levels were measured on each subject before and during the study and were found always to be in the normal range. Radioisotopes. CaCl. (20 pc) with a specific activity of 140 me’g and SrCl, (15 uc) carrier free were administered intravenously and simultaneously to each subject. Radiochemical assay. The concentration of Ca*? and Sr® in 24-hr urine and stool samples was measured daily for 10 days. The entire 24-hr urine and stool sainples were placed in tin cans, filled with water, sealed, and counted under an 8 inch x 4 inch Nal detector in the whole-body analyzer. connected to a 4o0-channel CA tones JUG? tub ¢e counter pulse-height @ =I: ,n) jal (7) where: f(t) represents a function, such as specific activity Ay; are the transition probabilities per unit time from jth into the ith compartment n his = — De ku (2) bgt Aoi represents loss from ith compartmentto outside For the mathematical analysis, the usual steady-state assumptions are made. These include the following: 7) the volumesof the compartments and the concentrations