Kroll, 2000

Model Structure

Pulsatile administration of the parathyroid hormone (PTH) has been shown to stimulate bone formation in both animals and humans, and the PTH signalling pathway is considered as a potential target for the development of new therapeutic treatments for post-menopausal osteoporosis. However, while pulsatile PTH exposure results in bone formation (deposition), paradoxically, it has been noted that continuous PTH administration causes net bone loss (resorption).

To date, the mechanisms underlying these two phenomena remain poorly understood, and in order to use PTH as a therapeutic treatment for osteoporosis it is essential that we improve our understanding of the dynamics of the PTH signalling pathway. To this end, Martin Kroll has developed a mathematical model which accounts for both net bone loss under conditions of continuous PTH administration, and also net bone formation with intermittent PTH administration. These two contrasting behaviours have been captured by describing the different effects of the hormone on the osteoblastic and osteoclastic populations of cells (as summarised in the figure below).

Schematic diagram of the effect of PTH on the development of osteoblasts. PTH binds to receptors on the preosteoblast precursors and stimulates their transition to preosteoblasts. However, PTH binding to these preosteoblasts inhibits their differentiation into osteoblasts, and IL-6 (which is secreted by the osteoblasts) is believed to enhance this inhibitory effect. The osteoblasts then differentiate into osteocytes at a rate which is dependent on their number. The IL-6 produced by the osteoblasts also stimulates the differentiation of preosteoclasts to osteoclasts. Osteoclasts become senescent at a rate dependent on their number.

The complete original paper reference is cited below:

Parathyroid hormone temporal effects on bone formation and resorption, Martin H. Kroll, 2000, Bulletin of Mathematical Biology , 62, 163-187. (A PDF version of the article is available to journal subscribers on the Bulletin of Mathematical Biology website.) PubMed ID: 10824426

It should be noted that in its current form, the CellML description of the this model is unable to perfectly capture the simulation results of the published model, this is due to the time delays which are difficult to describe in the CellML code.