Therapy discrimination via global sensitivity analysis of force-induced bone growth and adaptation

Identifying and discriminating plausible treatment targets for remodeling related bone disorders is a difficult task often involving medical studies and clinical experiments. We propose to apply a global sensitivity analysis approach to a mathematical model describing the process of force-induced bone growth and adaptation. The considered sensitivity analysis approach finds an outer bound on the set of possible steady states for regions of parameters and inputs/stimuli. The outer bounding is achieved by a reformulation as a feasibility problem, which is convexified and solved via a semidefinite program. In this work, besides the application of this method to the bone growth and adaptation model, we improve the outer bounds by using a smarter multidimensional bisection algorithm. The results obtained allow for structure discrimination between different treatment therapies with a preferable counteractive effect in relation to the severity degree of the bone loss condition.