The effect of surface area digitizations on the prediction of spherical anatomical geometries for computer-assisted applications

Intraoperative digitization of osseous structures is an integral component of computer-assisted orthopaedic surgery. This study determined the repeatability and accuracy of predicting known radii and center locations of spherical objects for different proportions of digitized surface areas and various sphere sizes. Also, we investigated these accuracies for some relevant near-spherical osseous structures where results from full area digitizations were considered to be true. Digitizations were performed using an electromagnetic tracker with a stylus on the total and fractional surfaces of 10 hemispheres, ranging from 10 to 28 mm in radius. Repeatability was quantified by digitizing five trials of the entire surface and various fractional areas of selected hemisphere sizes. Similar trials were conducted on models of a humeral and femoral head, using the full head area as baseline and digitizing 15 and 30 mm diameter areas of the full head. Mean error for the predicted radii and center positions of the hemispheres ranged from 0.39±0.29 to 0.14±0.07 mm and 0.52±0.31 to 0.22±0.12 mm, respectively. Repeatability for the predicted radii and centers produced maximum standard deviations of 0.31 and 0.42 mm, respectively. All errors decreased as fractional area (40%, 60%, 80% and 100%) increased (p<0.05). Radius of curvature and center position errors for the humeral head model were 1.51±2.11 and 2.28±1.51 mm, respectively. These errors for the femoral head model were 3.37±4.14 and 4.25±4.14 mm, respectively. Errors resulting from the prediction of radius and center indicate that non-spherical anatomical structures are more sensitive to the digitized area, and hence digitization of the largest surface possible seems warranted.