An integer programming model for distal humerus fracture fixation planning

Abstract

Objective: To demonstrate the feasibility of an integer programming model to assist in pre-operative planning for open reduction and internal fixation of a distal humerus fracture.Materials and Methods: We describe an integer programming model based on the objective of maximizing the reward for screws placed while satisfying the requirements for sound internal fixation. The model maximizes the number of bicortical screws placed while avoiding screw collision and favoring screws of greater length that cross multiple fracture planes.Results: The model was tested on three types of total articular fractures of the distal humerus. Solutions were generated using 5, 9, 21 and 33 possible screw orientations per hole. Solutions generated using 33 possible screw orientations per hole and five screw lengths resulted in the most clinically relevant fixation plan and required the calculation of 1,191,975 pairs of screws that resulted in collision. At this level of complexity, the pre-processor took 104 seconds to generate the constraints for the solver, and a solution was generated in under one minute in all three cases.Conclusion: Despite the large size of this problem, it can be solved in a reasonable amount of time, making use of the model practical in pre-surgical planning.