Computer modelling of bone fracture healing: a novel structural optimization approach

Abstract

The present work suggests a possible future direction for computational modelling of bone fracture healing which can aid the clinicians in assessment and treatment of bone fractures. In particular, the focus lies on introducing goal-based emulation of the complete healing process so that all the stages in fracture healing such as callus formation, mineralization and remodelling could be simulated using a single governing principle. This work tests one such approach where bone cross-section development and its repair is hypothesized to be governed by the principle of minimum potential or free energy (second law of thermodynamics). The hypothesis is validated with the help of a novel structural topology optimization method where total strain energy of a structure is minimized against a polar first moment of area/mass constraint. The new topology optimization method is employed to find optimal cross-sections for the mid-diaphysis of a long bone under loading conditions specific to different developmental stages. The optimized bone sections are similar to those observed experimentally. As the next step, a similar approach was used to predict day-wise callus distribution and mineralization during healing of a cross-section which is damaged due to a miniature fracture called cortical bone (or drill-hole) defect. The preliminary results show experimentally similar fracture callus distribution and resorption during the course of healing. This encourages to further explore the devised algorithm for emulating three-dimensional callus distribution, mineralization and resorption which is limited to only transverse directions (i.e., cross-section) in this work. The current topology optimization formulation can be used to develop a Graphical User Interface (GUI) based tool where the course of healing could be pre-simulated for different fixator types, their orientations and screwing positions. Such pre-vi simulation would only require the computed tomography (CT) data of the fracture and therefore, would aid the clinicians by letting them choose the most suitable surgical intervention.