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A mathematical model for bone healing predictions under the ultrasound effect

The bone healing process involves a sequence of cellular actions and interactions, regulated by biochemical and mechanical signals. Experimental studies have shown that ultrasound accelerates bone solidification and enhances the underlying healing mechanisms. We present a mathematical model for deriving predictions of bone healing under the presence of ultrasound. The model consists of i) partial differential equations which describe the spatiotemporal evolution cells, growth factors, tissues and ultrasound acoustic pressure and ii) velocity equations of endothelial tip cells which determine the development of the blood vessel network. The results showed that ultrasound accelerates bone healing primarily by enhancing blood vessel growth. Thus the proposed model could be useful for the ultrasonic evaluation of bone fracture healing.