MRI Registration for Human Hip Kinematics

Measurement of joint kinematics can provide knowledge to help improve joint prosthesis design, as well as identify joint motion patterns that may lead to joint degeneration or injury. More investigation into how the hip translates in live human subjects during high amplitude motions is needed. This work presents a design of a non-invasive method using the registration between images from conventional Magnetic Resonance Imaging (MRI) and open MRI to calculate three dimensional hip joint kinematics. The method was tested on a single healthy subject in three different poses. MRI protocols for the conventional gantry, high-resolution MRI and the open gantry, lowresolution MRI were developed. The scan time for the low-resolution protocol was just under 6 minutes. High-resolution meshes and low resolution contours were derived from segmentation of the high-resolution and low-resolution images, respectively. Low-resolution contours described the poses as scanned, whereas the meshes described the bones’ geometries. The meshes and contours were registered to each other, and joint kinematics were calculated. The segmentation and registration were performed for both cortical and sub-cortical bone surfaces. A repeatability study was performed by comparing the kinematic results derived from three users’ segmentations of the sub-cortical bone surfaces from a low-resolution scan. The root mean squared error of all registrations was below 1.92mm. The maximum range between segmenters in translation magnitude was 0.95mm, and the maximum deviation from the average of all orientations was 1.27◦. This work demonstrated that this method for non-invasive measurement of hip kinematics is promising for measuring high-range-of-motion hip motions in vivo.

Distributed Extremum-Seeking Control with Applications to High-Altitude Balloons

The real-time optimization of large-scale systems is a difficult problem due to the need for complex models involving uncertain parameters and the high computational cost of solving such problems by a decentralized approach. Extremum-seeking control (ESC) is a model-free real-time optimization technique which can estimate unknown parameters and can optimize nonlinear time-varying systems using only a measurement of the cost function to be minimized. In this thesis, we develop a distributed version of extremum-seeking control which allows large-scale systems to be optimized without models and with minimal computing power. First, we develop a continuous-time distributed extremum-seeking controller. It has three main components: consensus, parameter estimation, and optimization. The consensus provides each local controller with an estimate of the cost to be minimized, allowing them to coordinate their actions. Using this cost estimate, parameters for a local input-output model are estimated, and the cost is minimized by following a gradient descent based on the estimate of the gradient. Next, a similar distributed extremum-seeking controller is developed in discrete-time. Finally, we consider an interesting application of distributed ESC: formation control of high-altitude balloons for high-speed wireless internet. These balloons must be steered into a favourable formation where they are spread out over the Earth and provide coverage to the entire planet. Distributed ESC is applied to this problem, and is shown to be effective for a system of 1200 ballons subjected to realistic wind currents. The approach does not require a wind model and uses a cost function based on a Voronoi partition of the sphere. Distributed ESC is able to steer balloons from a few initial launch sites into a formation which provides coverage to the entire Earth and can maintain a similar formation as the balloons move with the wind around the Earth.