Bisphosphonates (BPs) are used to mitigate osteoporosis in patients who are at high risk for bone fractures. Common methods of administration of BPs rely on systemic delivery, which can lead to abdominal discomfort and unwanted concentrations of drug in other areas of the body. However, there is a limited understanding of the diffusion of BPs via localized delivery from scaffolds. This study investigates the diffusion of alendronate, a commonly used BP, from a scaffold into bone.

A model for diffusion with fluid flow was constructed using the commercially available computational software COMSOL. The femur bone is approximated as a 3D cylinder of length 0.1 m with four layered subdomains: scaffold, periosteum, compact bone, and marrow. The layers are of radius 0.0002 meters, 0.00022 meters, 0.001 meters, and 0.0138 meters respectively. BPs have a diffusion constant of 115·10-12 square meters per second, 2.44·10-10 square meters per second, 2.44·10-10 square meters per second, and 1·10-12 square meters per second respectively in the four layers of the domain. The periosteum and compact bone have capillaries that run the length of the domain. These are modeled as randomly distributed identical cylinders running the length of the domain with a unidirectional fluid flow of 5·10-5 meters per second with a fluid density of 1060 kilograms per cubic meter. The initial conditions are concentration of 0 everywhere expect for the scaffold subdomain which has an initial concentration of 0.018 moles of alendronate per cubic meter of bone. These values can be found in Appendix A, Table 2.

The results of this model show the concentration of bound alendronate in the bone reaches an effective concentration of 1·10-4 moles per cubic meter before 10 hours. We have also found the bound alendronate fraction has a low dependency on the initial scaffold concentration with the bound alendronate fraction at over 90% alendronate clearance time being over 0.8 for varying initial concentrations.

Sensitivity analysis revealed that bound alendronate concentration is not dependent on the diffusivities of compact bone or marrow, or on blood velocity, but is highly dependent on initial scaffold concentration and the binding rate constant of alendronate to bone.

This model provides a comprehensive understanding of how BPs move through the bone and the time it takes for BP concentration to reach certain levels in the bone. This in turn allows for more accurate dosage times and amounts in order to provide the most efficient bone loss prevention.