Dynamic modeling of bone metastasis, microenvironment and therapy: Integrating parathyroid hormone (PTH) effect, anti-resorptive and anti-cancer therapy

• A model for bone remodeling that includes PTH is proposed.
• PTHrP is included to account for the vicious cycle of bone metastases.
• PK/PD of bisphosphonates, denosumab and chemotherapy are included as treatment.
• Model simulations illustrate how anti-cancer and anti-resorptive therapies on bone metastases can reduce tumor burden and restore bone health.

Bone is a common site for the development of metastasis, as its microenvironment provides the necessary conditions for the growth and proliferation of cancer cells. Several mathematical models to describe the bone remodeling process and how osteoclasts and osteoblasts coupled action ensures bone homeostasis have been proposed and further extended to include the effect of cancer cells. The model proposed here includes the influence of the parathyroid hormone (PTH) as capable of triggering and regulating the bone remodeling cycle. It also considers the secretion of PTH-related protein (PTHrP) by cancer cells, which stimulates the production of receptor activator of nuclear factor kappa-B ligand (RANKL) by osteoblasts that activates osteoclasts, increasing bone resorption and the subsequent release of growth factors entrapped in the bone matrix, which induce tumor growth, giving rise to a self-perpetuating cycle known as the vicious cycle of bone metastases. The model additionally describes how the presence of metastases contributes to the decoupling between bone resorption and formation. Moreover, the effects of anti-cancer and anti-resorptive treatments, through chemotherapy and the administration of bisphosphonates or denosumab, are also included, along with their corresponding pharmacokinetics (PK) and pharmacodynamics (PD). The simulated models, available at http://sels.tecnico.ulisboa.pt/software/, are able to describe bone remodeling cycles, the growth of bone metastases and how treatment can effectively reduce tumor burden on bone and prevent loss of bone strength.