Evaluating treatment of osteoporosis using particle swarm on a bone remodelling mathematical model

Abstract

Bone loss in osteoporosis, commonly observed in postmenopausal women and the elderly, is caused by an imbalance in activities of bone-forming osteoblasts and bone-resorbing osteoclasts. To treat osteoporosis and increase bone mineral density (BMD), physical activities and drugs are often recommended. Complex systems dynamics prevent an intuitive prediction of treatment strategies, and little is known about an optimal sequence for the combinatorial use of available treatments. In this study, the authors built a mathematical model of bone remodelling and developed a treatment strategy for mechanical loading and salubrinal, a synthetic chemical agent that enhances bone formation and prevents bone resorption. The model formulated a temporal BMD change of a mouse's whole skeleton in response to ovariectomy, mechanical loading and administration of salubrinal. Particle swarm optimisation was employed to maximise a performance index (a function of BMD and treatment cost) to find an ideal sequence of treatment. The best treatment was found to start with mechanical loading followed by salubrinal. As treatment costs increased, the sequence started with no treatment and usage of salubrinal became scarce. The treatment strategy will depend on individual needs and costs, and the proposed model is expected to contribute to the development of personalised treatment strategies.