Beschreibung:
<jats:p>The role of imaging and image guidance is increasing in surgery and therapy, including treatment planning and follow‐up. Fluoroscopy is used for two‐dimensional (2D) guidance or localization; however, many procedures would benefit from three‐dimensional (3D) guidance or localization. Three‐dimensional computed tomography (CT) using a C‐arm mounted x‐ray image intensifier (XRII) can provide high‐quality 3D images; however, patient dose and the required acquisition time restrict the number of 3D images that can be obtained. C‐arm based 3D CT is therefore limited in applications for x‐ray based image guidance or dynamic evaluations. 2D‐3D model‐based registration, using a single‐plane 2D digital radiographic system, does allow for rapid 3D localization. It is our goal to investigate—over a clinically practical range—the impact of x‐ray exposure on the resulting range of 3D localization precision. In this paper it is assumed that the tracked instrument incorporates a rigidly attached 3D object with a known configuration of markers. A 2D image is obtained by a digital fluoroscopic x‐ray system and corrected for XRII distortions <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0001.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0001" /> and mechanical C‐arm shift <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0002.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0002" />. A least‐square projection‐Procrustes analysis is then used to calculate the 3D position using the measured 2D marker locations. The effect of x‐ray exposure on the precision of 2D marker localization and on 3D object localization was investigated using numerical simulations and x‐ray experiments. The results show a nearly linear relationship between 2D marker localization precision and the 3D localization precision. However, a significant amplification of error, nonuniformly distributed among the three major axes, occurs, and that is demonstrated. To obtain a 3D localization error of less than <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0003.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0003" /> for an object with <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0004.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0004" /> marker spacing, the 2D localization precision must be better than <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0005.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0005" />. This requirement was met for all investigated nominal x‐ray exposures at <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0006.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0006" /> FOV, and for all but the lowest two at <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0007.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0007" /> FOV. However, even for those two nominal exposures, the expected 3D localization error is less than <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0008.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0008" />. The tracking precision was <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0009.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0009" /> for the out‐of‐plane translations, <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0010.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0010" /> for in‐plane translations, and <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0011.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0011" /> for the rotations. The root mean square (RMS) difference between the true and projection‐Procrustes calculated location was <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mp1167-math-0012.png" xlink:title="urn:x-wiley:00942405:media:mp1167:mp1167-math-0012" />. It is believed these results show the potential of this technique for <jats:italic>dynamic</jats:italic> evaluations or <jats:italic>real‐time</jats:italic> image guidance using a single x‐ray source and XRII detector.</jats:p>