A study on the theoretical and practical accuracy of conoscopic holography-based surface measurements: toward image registration in minimally invasive surgery

Abstract

Background: Registered medical images can assist with surgical navigation and enable image-guided therapy delivery. In soft tissues, surface-based registration is often used and can be facilitated by laser surface scanning. Tracked conoscopic holography (which provides distance measurements) has been recently proposed as a minimally invasive way to obtain surface scans. Moving this technique from concept to clinical use requires a rigorous accuracy evaluation, which is the purpose of our paper.

Methods: We adapt recent non-homogeneous and anisotropic point-based registration results to provide a theoretical framework for predicting the accuracy of tracked distance measurement systems. Experiments are conducted a complex objects of defined geometry, an anthropomorphic kidney phantom and a human cadaver kidney.

Results: Experiments agree with model predictions, producing point RMS errors consistently < 1 mm, surface-based registration with mean closest point error < 1 mm in the phantom and a RMS target registration error of 0.8 mm in the human cadaver kidney.

Conclusions: Tracked conoscopic holography is clinically viable; it enables minimally invasive surface scan accuracy comparable to current clinical methods that require open surgery.

Figure 1

Conoscopic surface measurement through a laparoscopic port. The surgeon sweeps the laser over the tissue to measure the surface for image registration. The conoscopic holography sensor is optically tracked

Figure 2

(a) Anisotropic localization error of an optical tracking system measuring four fiducials. (b) A 1D conoscopic holography sensor is characterized by a focal length f and a working range [−Δ/2, Δ/2] around the focal spot

Figure 3

Calibration of a 1D conoscopic holography sensor. (a) The calibration parameters are the offset vector l to the lens frame L and the laser direction d̂ in the local coordinate frame C of the sensor. (b) To determine the calibration parameters, a point p, known with respect to the world coordinate frame W, is measured by the conoscopic holography sensor from different locations. The local coordinate frame C_i of the sensor is measured as T_i with respect to the world coordinate frame W. Additionally, the corresponding laser distance measurements d_i are recorded

Figure 4

System components. (a) A 1D conoscopic holography sensor is affixed to an optical bench, using an articulated holding arm. The spatial location of the conoprobe is optically tracked, using the attached rigid body with respect to a fixed reference frame, represented by the rigid body on the left. (b) A prototype attachment for laparoscopic applications. (c) A step phantom with adhesive cross marks (green) and divots (red circles). Divots are measured using a tracked point probe for point-based registration

Figure 5

Conoscopic surface measurement of a human ex vivo kidney covered in perirenal fat

Figure 6

Surface model of the anthropomorphic kidney phantom in the image coordinate system I (left) and the conoscopic surface measurement acquired in the patient coordinate system P (right). After successful surface-based registration, the measured point can be transformed into the image coordinate system using ^IT_P (bottom)

Figure 7

Convergence behaviour of the calibration. The RMSE is plotted against the number of data points (n) used for calibration. The dashed line is the convergence function $2.7{\sqrt{n}}^{-1}$

Figure 8

Example results of the surface registration. The left column indicates colour-coded FRE values and the right column colour-coded TRE values. (a, b) Step phantom; (c, d) anthropomorphic kidney phantom; (e, f) human ex vivo cadaver kidney covered in perirenal fat