Burton Ma

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Research

My research interests are in the area of computer-assisted surgery: image processing, image registration, visualization, surgical planning, error analysis, and applications of computer assistance in orthopaedic surgery.

Line-Based Ultrasound Calibration

We present an ultrasound calibration framework that is guided by the prediction of target registration error (TRE). Between successive measurements of the calibration phantom, our algorithm predicts how to position and orient the calibration phantom to collect the subsequent ultrasound fiducial to maximize the minimization of the predicted TRE. To accomplish this, we first introduced an oriented-line calibration phantom and modelled the ultrasound calibration process as a point-to-line iterative closest point registration problem. We then derived a spatial stiffness model for point-to-line registration. Assuming the fiducial localization error is isotropic and identical, the spatial stiffness model estimates the TRE for each pixel based on the current calibration estimate. We then search through the calibration tool space to find the pose (orientation and position) that, if the next fiducial is to be collected at this pose, the TRE is maximally minimized. Both the simulation and experimental results suggest that TRE decreases monotonically, reaching an asymptote when more than 12 measurements are made. Independent point reconstruction accuracy assessment showed sub-millimeter accuracy of the proposed calibration framework.

Line-Based Target Registration Error

We present a novel method for estimating target registration error (TRE) in point-to-line registration. We develop a spatial stiffness model of the registration problem and derive the stiffness matrix of the model which leads to an analytic expression for predicting the root-mean-square (RMS) TRE. Under the assumption of isotropic localization noise, we show that the stiffness matrix for line-based registration is equal to the difference of the stiffness matrices for fiducial registration and surface-based registration. The expression for TRE is validated in the context of freehand ultrasound calibration performed using a tracked line fiducial as a calibration phantom. Measurements taken during calibration of a tracked linear ultrasound probe were used in simulations to assess TRE of point-to-line registration and the results were compared to the values predicted by the analytic expression. The difference between predicted and simulated RMS TRE magnitude for targets near the centroid of the registration points was less than 5% of the simulated magnitude when using more than 6 registration points. The difference between predicted and simulated RMS TRE magnitude for targets over the entire ultrasound image was almost always less than 10% of the simulated magnitude when using more than 10 registration points. TRE magnitude was minimized near the centroid of the registration points and the isocontours of TRE were elliptic in shape.

Point-Based Target Registration Error

Guidance systems used for image guided surgery register data collected in real time (i.e. the position of a hand-held probe) to preoperative images to help guide a minimally invasive surgery. In the process of registration, the distances between corresponding points, representing the target registration error (TRE), is the most important error measure.

Finding TRE with noisy data points

Data points that are collected will each have a corresponding noise. Given the task of registering these noisy points to a rigid body, to estimate the root mean square target registration error, we came up with an analytic equation.

To then test the accuracy of this equation, we ran numerous registration simulations using both synthetic and real data points and models. The synthetic model was that of an ellipsoid, and random noise was added to points drawn from the surface of the ellipsoid. For the measured data points, we used plastic bone replicas and an optical tracking system. After gathering many data points on the bone using the tracking system, we performed registration of these points onto a 3D model of the plastic bones, which was produced with a CT scan.

Individualized Instrumentation for Distal Radius Osteotomy

The radius is the most commonly fractured bone in the arm. In cases where the fractured radius heals in an abnormal position, surgical treatment may be required to correct the deformity and restore the function of the wrist joint. Distal radius osteotomy involves cutting the radius near the original fracture site, rotating and translating the distal fragment to restore normal radiograpic alignment, filling the resulting gap with bone graft or substitute, and then securing the assembly with a metal plate and screws. In conventional technique, the alignment is achieved under fluoroscopic (x-ray) guidance. We've designed and tested a 3D printed indvidualized guide that fits onto to the patient's radius and provides navigational guidance of the fixation screws so that when the radius is cut and plated the pre-drilled holes align to the holes in the fixation plate.

Distraction Osteogenesis with a Taylor Spatial Frame

Rotational and translational deformities in the long bones can be corrected using distraction osteogenesis, developed by Russian orthopaedic surgeon Gavril Ilizarov. Ilizarov's method is based on the biological principle of inducing new bone growth by gradually distracting a fracture at regular intervals. More specifically, the method is achieved by performing a corticotomy or osteotomy on the deformed bone, fixating the distressed bone with a mechanical fixator, and distracting the bone according to a set schedule of corrections. We have developed a computer-assisted technique that modifies the conventional approach to deformity correction, using the Ilizarov method in four fundamental ways. (1) The need for the surgeon to preoperatively compute the frame parameters is removed. (2) The performed correction is based on the actual location of the frame with respect to the anatomy; any translational or angular malalignments that occur while mounting the frame are compensated for immediately, thereby potentially removing the need for residual correction. (3) The correction is calculated based on 3D coordinates from CT data, rather than measured from radiographs. (4) The surgeon has flexibility in frame placement; hence, anatomical constraints that may not have been apparent preoperatively can be compensated for in surgery.