A six-degree-of-freedom acoustic transducer for rotation and translation measurements across the knee

An acoustic transducer design to measure the relative translations and rotations across the knee with no mechanical coupling between the tibia and femur is presented. Platforms attached to femoral and tibial tracking fixtures hold acoustic sources and receivers, respectively. The distance from each source to each receiver is measured by the acoustic transit time and the translations and rotations across the knee joint are computed. For rotations less than 30 deg around the expected operating position, the resolution of the transducer is 0.3 deg; for translations less than 1.5 cm around the expected operating position, the resolution is 0.03 cm. Theoretical error analysis using a Monte Carlo method shows that the uncertainty in the measurement depends on the relative position of the sources and receivers. The analysis predicts the worst case resolution of the transducer as 0.09 cm in translation and 0.6 deg in rotation when the receiver platform is translated 8.0 cm parallel to the source platform. The transducer and fixturing system are demonstrated on a cadaver specimen for applied anterior force and applied internal-external rotation. Errors due to (soft tissue) motion of the transducer relative to the bone during in vivo measurements are assessed on the cadaver specimen. For internal-external rotation the error due to soft tissue motion is a maximum of 0.5 cm in translation and 1.8 deg in rotation. For applied anterior force the error due to soft tissue motion is a maximum of 0.16 cm in translation and 2.7 deg in rotation.