Interpretation of 41Ca data using compartmental modeling in post-menopausal women

Abstract

Calcium-41 (t(1/2) = 10(5) years) can be used after a single dose to follow calcium metabolism over a subject's lifetime. The aims of this study were to expand a (41)Ca kinetic model and estimate bone resorption in women with stable bone loss, compare the rates with those calculated with classical isotope studies, and to use the model to simulate dynamic changes in urinary (41)Ca:Ca ratios and bone balance for the design and interpretation of (41)Ca studies. Forty-two women >5 years post-menopause were given (41)Ca intravenously. Bone mineral content and bone mineral density of total body were measured by dual-energy X-ray absorptiometry at the beginning of the study. Urine collections were made periodically for up to ~5 years while subjects were free living. Urinary (41)Ca:Ca ratios were measured using accelerator mass spectrometry. The isotope data were analyzed by compartmental modeling. Four compartments were necessary to fit the urinary tracer data and total bone calcium. The final model included pathways for absorption, distribution, urinary excretion, and endogenous excretion and was used to calculate rates of bone turnover. Estimates of bone resorption in a subset of the women (n = 13), studied previously in a 3-week balance and full kinetic study with (45)Ca, agreed with those using (41)Ca methodology. Thus, rates of bone resorption can be estimated from (41)Ca urinary data in stable post-menopausal women. The model was used to simulate dynamic changes in urinary (41)Ca:Ca ratios and bone balance, as a result of interventions that perturb calcium metabolism to aid in study design and interpretation.

Figures

Fig. 1

Compartmental model for calcium metabolism, with pools numbered arbitrarily with values for a fractional transfers (L(i,j), into compartment i from compartment j), mean±SD (n=42), b pool size and mass transfer, and c percent distribution of Ca from the compartments where the arrows start. L(6,1) was the average for subjects where urinary excretion was measured (n=17). Absorption [L(1,8)/(L(1,8)+L(10,8)] was fixed at 20%, and endogenous excretion, L(10,1), was based on a rate of 150 mg/day [14]. Compartment 4 was necessary to fit both urinary tracer and bone calcium data, and L(2,4) was fixed based on cortical bone turnover of 4.4%/year [16, 17]

Fig. 2

Calculated fits of the model (Fig. 1) (lines) to urine 41Ca:Ca ratio data (symbols) for three subjects. Triangle and square symbols indicate two subjects who received 1 μCi (right y-axis, 41Ca:Ca ratio×10−9), while diamond symbol indicates a subject who received 50 nCi (left y-axis, 41Ca:Ca ratio×10−10)

Fig. 3

Simulation of distribution of the initial dose (fraction) between pools for the model in Fig. 1 over 5,000 days. Compartment 4 has the slowest rate of turnover, which is consistent with “cortical” bone, suggesting that interventions at 250 days post-dose mainly affect tracer in “trabecular” bone

Fig. 4

Simulation of bone balance (the sum of “trabecular” and “cortical” bone balances) over time with a sustained intervention (increased calcium absorption, urine excretion, and “trabecular” bone deposition, simulation 8 in Table 3). For this case, the simulation predicts that total bone balance gain persists. It takes many years to return to the pre-intervention, or zero state