Measuring relative positions and orientations of the tibia with respect to the femur using one-channel 3D-tracked A-mode ultrasound tracking system: A cadaveric study

A Method to Track 3D Knee Kinematics by Multi-Channel 3D-Tracked A-Mode Ultrasound

This paper introduces a method for measuring 3D tibiofemoral kinematics using a multi-channel A-mode ultrasound system under dynamic conditions. The proposed system consists of a multi-channel A-mode ultrasound system integrated with a conventional motion capture system (i.e., optical tracking system). This approach allows for the non-invasive and non-radiative quantification of the tibiofemoral joint's six degrees of freedom (DOF). We demonstrated the feasibility and accuracy of this method in the cadaveric experiment. The knee joint's motions were mimicked by manually manipulating the leg through multiple motion cycles from flexion to extension. To measure it, six custom ultrasound holders, equipped with a total of 30 A-mode ultrasound transducers and 18 optical markers, were mounted on various anatomical regions of the lower extremity of the specimen. During experiments, 3D-tracked intra-cortical bone pins were inserted into the femur and tibia to measure the ground truth of tibiofemoral kinematics. The results were compared with the tibiofemoral kinematics derived from the proposed ultrasound system. The results showed an average rotational error of 1.51 ± 1.13° and a translational error of 3.14 ± 1.72 mm for the ultrasound-derived kinematics, compared to the ground truth. In conclusion, this multi-channel A-mode ultrasound system demonstrated a great potential of effectively measuring tibiofemoral kinematics during dynamic motions. Its improved accuracy, nature of non-invasiveness, and lack of radiation exposure make this method a promising alternative to incorporate into gait analysis and prosthetic kinematic measurements later.

Improving ultrasound-based bone registration using the iterative closest point algorithm paired with a complex optimization solver

The Iterative Close Point (ICP) algorithm is used for bone registrations based on ultrasound measurements. However, the ICP has been shown to suffer from local minima. The Complex optimization, as a more robust routine compared to the commonly used gradient-based algorithms, could be an alternative for solving the ICP problem. In this study, we investigated the effect of the initial estimate and the number of registration points on bone registrations achieved using the ICP and a Complex optimization routine and we compared it against using Quadratic Sequential Programming (SQP). Ultrasound measurements were performed with an A-mode probe on a bovine humerus and an ovine femur embedded into ballistic gel. Simultaneously, the bones and the probe were tracked in 3D space using retroreflective markers. Kinematic, ultrasound and geometrical data obtained from scans of the specimens and the probe served as input to a bone registrations routine. Registrations were performed using two ICP solvers for different initial estimates and number of registration points. On average, 68 % of the Complex optimization registrations had less than 1 mm translation error and less than 1° rotational error for perturbations of the initial estimate from the reference measurements compared to the 35 % of the SQP ones. Similar medians of registration errors were observed between the two methods for variations of the number of the employed registration points. Although the Complex optimization provided accurate bone registrations for all cases, the objective function could not always determine the registrations with the smallest registration error. Future research should explore methodologies to overcome this challenge.