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TECHNICAL PAPERS: Joint/Whole Body

# Theoretical Accuracy of Model-Based Shape Matching for Measuring Natural Knee Kinematics with Single-Plane Fluoroscopy

[+] Author and Article Information
Benjamin J. Fregly1

Department of Mechanical and Aerospace Engineering, Department of Biomedical Engineering, Department of Othopaedics and Rehabilitation, University of Florida, Gainesville, FL 32611fregly@ufl.edu

Haseeb A. Rahman

Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611

Scott A. Banks

Department of Mechanical and Aerospace Engineering, Department of Orthopaedics and Rehabilitation, University of Florida, Gainesville, FL 32611 and The Biomotion Foundation, West Palm Beach, FL 33480

1

Corresponding author.

J Biomech Eng 127(4), 692-699 (Jan 27, 2005) (8 pages) doi:10.1115/1.1933949 History: Received January 05, 2004; Revised January 27, 2005

## Abstract

Quantification of knee motion under dynamic, in vivo loaded conditions is necessary to understand how knee kinematics influence joint injury, disease, and rehabilitation. Though recent studies have measured three-dimensional knee kinematics by matching geometric bone models to single-plane fluoroscopic images, factors limiting the accuracy of this approach have not been thoroughly investigated. This study used a three-step computational approach to evaluate theoretical accuracy limitations due to the shape matching process alone. First, cortical bone models of the femur, tibia/fibula, and patella were created from CT data. Next, synthetic (i.e., computer generated) fluoroscopic images were created by ray tracing the bone models in known poses. Finally, an automated matching algorithm utilizing edge detection methods was developed to align flat-shaded bone models to the synthetic images. Accuracy of the recovered pose parameters was assessed in terms of measurement bias and precision. Under these ideal conditions where other sources of error were eliminated, tibiofemoral poses were within $2mm$ for sagittal plane translations and $1.5deg$ for all rotations while patellofemoral poses were within $2mm$ and $3deg$. However, statistically significant bias was found in most relative pose parameters. Bias disappeared and precision improved by a factor of two when the synthetic images were regenerated using flat shading (i.e., sharp bone edges) instead of ray tracing (i.e., attenuated bone edges). Analysis of absolute pose parameter errors revealed that the automated matching algorithm systematically pushed the flat-shaded bone models too far into the image plane to match the attenuated edges of the synthetic ray-traced images. These results suggest that biased edge detection is the primary factor limiting the theoretical accuracy of this single-plane shape matching procedure.

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## Figures

Figure 1

Segmentation of CT data to generate point clouds for geometric cortical bone models. (a) Sample CT image of the femur and patella. (b) Boundaries identified by the watershed algorithm. (c) Cortical bone contours defined from the segmentation.

Figure 2

Creation of polygonal cortical bone models from the point cloud data. (a) Segmented point clouds demonstrating the outer and inner cortical bone boundaries as well as the regions covered by the fine and coarse scans. (b) Polygonal surface models fitted to the point clouds using commercial reverse engineering software. (c) Cutaway view of polygonal models showing the outer and inner cortical surfaces of each bone.

Figure 3

Synthetic fluoroscopic image creation process to simulate an in vivo stair rise motion. (a) Sample experimental fluoroscopic image. (b) Femur, tibia/fibula, and patella bone models manually matched to the experimental image. (c) Corresponding synthetic fluoroscopic image generated by ray tracing the cortical bone models in their manually matched poses. (d) Femur, tibia/fibula, and patella bone models automatically matched to the synthetic image to evaluate the accuracy of the recovered pose parameters.

Figure 4

Synthetic fluoroscopic image creation process to simulate a wide array of random poses with the bone models in a fixed relative pose. (a) Experimental fluoroscopic image with manually matched bone models used to define the relative pose parameters for all random images. (b) Synthetic fluoroscopic image generated using ray tracing after application of a random transformation to the cortical bone models. (c) The same synthetic fluoroscopic image generated using flat shading instead of ray tracing to eliminate bone edge attenuation.

Figure 5

Univariate optimization using cubic curve fitting to account for noise in the cost function. (a) Example of a noisy cost function in one direction along with seven initial sampled points. (b) Shifted sampled points using the same spacing to move the lowest point to the middle. (c) Least-squares cubic curve fit of the sampled points to evaluate fit accuracy, adjust sampled point spacing if needed, and calculate the minimum analytically.

Figure 6

Automatic step size adjustment rationale to select sampled point spacing for an accurate cubic curve fit. Left axis is goodness of fit quantified using the adjusted R2 value, while right axis is noise quantified using the standard error of the estimate s. Four potential regions can be identified by combining R2 and s information: Region 1—R2<0.99, s<1; Region 2—R2>0.99, s<1; Region 3—R2>0.99, s>1; Region 4—R2<0.99, s>1. Knowledge of the region for the current fit can be used to adjust the sampled point spacing automatically (see text) until the fit is in region 2, where R2 is high and s is low.

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