Interpolation of three dimensional kinematics with dual-quaternions

Devising patient-specific kinematic assessment techniques are critical for both patient diagnosis and treatment evaluation of complex biomechanical joints within the body. New non-invasive kinematic assessment techniques, such as bi-planar fluoroscopic registration, provide improved insight on joint biomechanics compared to traditional techniques, but at the expense of higher radiation exposure to the patient. The purpose of this study was to minimize the x-ray sample size required for evaluating spine kinematics, ultimately reducing radiation exposure, while maintaining a high degree of accuracy by improving upon existing 3D kinematic interpolation techniques. Existing interpolation methods were improved to account for non-uniformly sampled control points and applied to new motion descriptors, thus creating a new approach to 3D kinematic interpolation utilizing dual-quaternions. Interpolation reconstruction methods were applied to decimated gold standard ex vivo spinal kinematic data originally acquired at 30 Hz. The effects of interpolation method and variables (motion descriptor, sample spacing, sampling correction factors) on accuracy were compared. Dual-quaternion interpolation methods and equal interval angular sampling showed superior reconstruction results. Accuracy also improved when using temporal correction factors. Less than 1% normalized root-mean-squared error and less than 2% normalized maximum error were achieved from 0.36% of the original data set. The new approach also demonstrated its scalability for larger movements. However, accuracy may vary when interpolating more complex motion patterns. Overall, multiple interpolation methods and factors were evaluated in reconstructing 3D spine kinematics. High accuracy at low sample sizes and advantageous scalability to motions with larger total displacement illustrate its viability for bi-planar fluoroscopy.