Mechanistic model for calcium treatment effect in calcium-parathyroid hormone homeostasis after thyroidectomy in Koreans.

Aims: This study aims to develop a mechanism-based model of calcium treatment effect in calcium-parathyroid hormone (PTH) homeostasis after thyroidectomy in Koreans and evaluate the potential covariates influencing on the kinetics of calcium and PTH concentration.

Methods: A retrospective data set for 1142 patients who underwent thyroidectomy in 2013 at Severance hospital was collected from electric medical records (EMR) system. Post-thyroidectomy calcium concentrations and PTH levels obtained under the treatment of calcium and vitamin D supplements were analyzed as dependent variables, and demographics and operation conditions were tested as potential covariates. Calcium concentrations were described using a turn-over model and PTH concentration was described using a precursor-dependent indirect response model, where PTH is produced from PTH precursor (PP) through first order kinetics and PTH stimulation is modulated by a negative feedback system, with PTH stimulation increasing when occupancy decreases and vice versa. Population modeling approach was performed using NONMEM 7.3.

Results: The effect of thyroidectomy on calcium and PTH concentrations were best described by immediate drop in calcium and PTH levels at time of surgery and then exponentially increase up to maximum recovery level, with difference between baseline and maximum recovery levels corresponding to unrecovered calcium and PTH concentrations. Treatment effect by exogenous calcium was then modeled to stimulate calcium production rate in turnover model. The parameter estimates were 9.19 mg/dl and 46.4 pg/ml for baseline calcium and PTH concentrations, 0.736/day and 0.626/day for recovery rate constants for calcium and PTH concentrations after thyroidectomy, 0.114 /day and 0.905 /day for fractional turn-over rates of calcium and PTH, 2180 L for volume of distribution of calcium compartment, and 0.26 mg/dL and 10.4 pg/ml for unrecovered calcium and PTH levels.

Conclusion: The developed model was adequately fitted to post-thyroidectomy calcium and PTH concentrations. Further studies will include evaluation of potential covariates on the kinetics of calcium and PTH.

References: Abraham AK, Mager DE, Gao X, Li M, Healy DR, Maurer TS. J Pharmacol Exp Ther. 2009 Jul;330(1):169-78.