Domain-independent simulation of physiologically relevant callus shape in mechanoregulated models of fracture healing

Mechanoregulatory models have been used to predict the progression of bone fracture healing for more than two decades. However, many published studies share the same fundamental limitation: callus development proceeds within a pre-defined domain that both restricts and directs healing and leads to some non-physiologic healing patterns. To address this limitation, we added two spatial proximity functions to an existing mechanoregulatory model of fracture healing to control the localization of callus within the healing domain. We tested the performance of the new model in an idealized ovine tibial osteotomy with medial plate fixation using three sizes of healing domains and multiple variations of the spatial proximity functions. All model variations produced outward callus growth and bridging weighted toward the far cortex, which is consistent with in vivo healing. With and without the proximity functions, there were marked differences in the predicted callus volume and shape. With no proximity functions, the callus produced was strongly domain dependent, with a 15% difference in volume between the smallest and largest initialization domains. With proximity function control, callus growth was restricted to near the fracture line and there was only 2% difference in volume between domain sizes. Superimposing both proximity functions – one to control outward growth and one representing a decay in periosteal activity away from the fracture – produced a predicted callus size that was within the physiologic range for sheep and had a realistic morphology when compared with fluorescent dye co-localization with calcium deposition over time and histology.