Date of Completion


Embargo Period



Vitamin D, pharmacokinetics, 25-hydroxylated vitamin D, 25OHD, mathematical models

Major Advisor

Marc Gastonguay

Associate Advisor

Kevin S. Brown

Associate Advisor

Yong-Jun Shin

Associate Advisor

Joseph A. Lorenzo

Associate Advisor

Matthew M. Riggs

Field of Study

Biomedical Engineering


Doctor of Philosophy

Open Access

Open Access


Objectives: Relationships between Vitamin D dose, 25OHD, and indicators of bone health (serum calcitriol, parathyroid hormone (PTH), and bone mineral density at the lumbar spine (BMDLS)) were explored by considering the combined effects of Vitamin D3 and calcium administration (D3CA) on bone-health endpoints.

Methods: Population PK models were developed to predict D and 25OHD, and the final model was integrated with a previously published MSPM, describing calcium, PTH, and bone-remodeling. Public-source D and 25OHD PK data in healthy or osteoporotic populations, including 74 studies, representing 5684 individuals, were selected using PUBMED. Nonlinear-mixed-effects models were developed simultaneously for D and 25OHD PK (NONMEM v7.2). Model development explored 1- and 2-compartment models with linear (CL) or non-linear (CLNL) clearance. Using R's mrgsolve package, a scaling factor for calcitriol production and exponent-gamma term, related to osteoclast bone resorption, were estimated, translating predicted changes in bone-markers to changes in BMDLS (Nelder-Mead method in stats R package). Population-level simulations evaluated changes in BMDLS/PTH, following various 1-year regimens of D3CA administration and quantified the relationship between BMDLS/PTH and 25OHD concentration.

Results: D2/D3 parent and metabolite were described by 2-compartment models with numerous shared estimates. D3 CLNL resulted in inverse 25OHD3 relationships with dose and baseline; D2 did not exhibit nonlinearity. A power-model structure described the 25OHD-calcitriol conversion (theta1 = 638.1, gamma= 0.038), reflecting the apparent self-inhibition of calcitriol on its own production.Consistent with known biology, results from population-level simulations indicated that, for fixed D3 doses, BMDLS/PTH increased/decreased with increasing calcium administration (BMDLS PCFB range: 0.1 to 1.7%; PTH PCFB range: -4 to -30% for D3 doses 400-5000 IU/d, calcium doses 0-300 mg/d for 1 year). Also, BMDLS/PTH changed by +2%/-52.7% for 25OHD concentrations 43-102 nmol/L.

Conclusions: This is the first model that simultaneously integrates D3/D2 data, describing the system kinetics as a single unit and the first to quantitatively evaluate D3CA administration effect on bone-health endpoints. Future utility of results includes comparing effects of D3 or D3CA administration during clinical trials of other anti-osteoporosis therapeutics and quantifying D3 effects in other disease states like renal osteodystrophy.