Kinematic simulation of fracture reduction and bone deformity correction under unilateral external fixation

Combined kinematic analysis and graphic models of two unilateral external fixators are presented to simulate and visualize the correction of bone fracture deformities through systematic adjustments of the fixator joints. The models were developed as rigid linkage systems, and the analysis utilized the 4x4 transformation matrices and the kinematic chain theory to obtain the necessary rotations and translations at each joint of the fixator to correct bone deformities at the fracture site. Three-dimensional malalignments with fracture gaps were simulated to correct the deformities. Due to the redundant pair variables in the fixator joints and other problems in obtaining unique solutions, an optimization technique was used to solve the governing linkage loop equations. For each adjustment solution, the bone correction paths were infinite but a unique and optimal reduction path was obtained by applying corrections to all joints simultaneously and in small increments. When the deformity exceeded a certain range, no admissible solution could be obtained, partially due to the limitation of the unilateral fixator configuration and partially due to the restricted joint rotation and translation in the fixator design. The present models and analysis technique can be used to investigate a fixator's adjustability to correct a 3-D bone deformity at a fracture or lengthening site facilitating patient care planning and medical personnel training.