Optimal Control and Cost-Effectiveness Analysis of Porosity-Driven Bone Remodeling Dynamics

This paper develops an optimal control framework for a mechanical–structural model of bone remodeling that couples osteocytes, osteoblasts, and osteoclasts with bone density, incorporating porosity-dependent feedback mechanisms. To represent clinically relevant interventions, three bounded control functions are introduced: anabolic stimulation of osteoblast activity, anti-resorptive suppression of osteoclast-mediated resorption, and structural modulation of porosity feedback. The controlled system is shown to be mathematically well-posed, and the necessary optimality conditions are derived via Pontryagin’s Maximum Principle, leading to explicit characterizations of the optimal controls. The resulting state–adjoint system is solved numerically using a forward–backward sweep method. Numerical results demonstrate that the optimal intervention effectively suppresses osteoclast activity and drives the system toward higher, more stable bone density levels than the uncontrolled dynamics. In particular, the anti-resorptive control consistently plays the dominant role in shaping the optimal strategy. A cost-effectiveness analysis based on ACER, ICER, and the efficient frontier shows that strategies involving anti-resorptive inhibition achieve the greatest therapeutic gains at moderate cost, while additional controls yield only marginal improvements. Sensitivity analysis further indicates that parameters associated with osteoclast dynamics and bone formation have the strongest influence on density-related outcomes.