A Model-Based Approach to Diagnosing Hypercalcemia

The more common hypercalcemia-causing pathologies, primary hyperparathyroidism (PHPT), humoral hypercalcemia of malignancy (HHM), and familial benign hypercalcemia (FBH), have similar pathophysiologies. Currently, there are no standardized tests to differentiate among them. Using our previously developed computational models of physiological calcium regulation in healthy, FBH, PHPT, and HHM, this follow-up paper presents a model-based approach for differentially diagnosing these three pathologies. Additionally, for PHPT, our approach allows for predicting the size of PTG adenomatous growth and for inferring the stage of PHPT (early-to-mid stage or mid-to-late stage). Each model was subjected to 2-h calcium infusion while the intra-and postinfusion calciotropic response profiles of plasma Ca, PTH, calcitriol (CTL), and urinary Ca (Cau) were analyzed using control engineering concepts. Our research showed that two model parameters -minimum PTH secretory rate (ACa(s),r) and hypercalcemic slope (mCa(s)A)-and the four metrics of Ca settling time, PTH and CTL suppression, and maximum urinary Ca ratio were sufficient to provide distinct differentiating characteristics across the three pathologies. Furthermore, in the case of PHPT, estimates of minimum PTH secretory rate and the level of PTH suppression observed were found to correlate with postsurgical PTG adenoma mass. The minimum PTH secretory rate increases from healthy to FBH to PHPT and is inconsequential in HHM. Also, for PHPT, the minimum PTH secretory rate increases with PTG adenomatous growth. Likewise, the hypercalcemic slope is similar in healthy and FBH; decreases with increasing PTG mass in PHPT; and is inconsequential in HHM. Both PTH and CTL suppression were highest in healthy and FBH, lower in PHPT (with decreasing levels as PTG adenoma increases), and lowest in HHM. Finally, the Ca settling time and maximum urinary Ca ratio were the lowest for healthy and FBH, increased with increasing stage of PHPT, and were highest in HHM. For PHPT, a series of three relationships is derived between PTH suppression, minimum PTH secretory rate, and PTG mass such that the PTG mass can be inferred from the observed PTH suppression. The method and results herein have aided in the development of a set of observations (seven in total) that can serve as a guide to the research clinician for making a quick preliminary diagnosis across the three pathologies.