Design and validation of an open-source library of dynamic reference frames for research and education in optical tracking

Abstract

Dynamic reference frames (DRFs) are a common component of modern surgical tracking systems; however, the limited number of commercially available DRFs poses a constraint in developing systems, especially for research and education. This work presents the design and validation of a large, open-source library of DRFs compatible with passive, single-face tracking systems, such as Polaris stereoscopic infrared trackers (NDI, Waterloo, Ontario). An algorithm was developed to create new DRF designs consistent with intra- and intertool design constraints and convert to computer-aided design (CAD) files suitable for three-dimensional printing. A library of 10 such groups, each with 6 to 10 DRFs, was produced and tracking performance was validated in comparison to a standard commercially available reference, including pivot calibration, fiducial registration error (FRE), and target registration error (TRE). Pivot tests showed calibration error [Formula: see text], indistinguishable from the reference. FRE was [Formula: see text], and TRE in a CT head phantom was [Formula: see text], both equivalent to the reference. The library of DRFs offers a useful resource for surgical navigation research and could be extended to other tracking systems and alternative design constraints.

Keywords: dynamic reference frames; open-source; optical tracking; surgical navigation; three-dimensional printing.

Fig. 1

Illustration of tool design parameters and constraints. (a) Intrabody tool constraint: lengths must differ by at least $|\nabla d_{\min }|=5\mathrm{mm}$. (b) Interbody tool constraint: for similar length pairs between tools ($<5\mathrm{mm}$ difference in length), the angles must differ by ${\theta }_{\min }=2\mathrm{deg}$. (c) Example DRF (NDI #8700339) used as a reference in experiments throughout this work, annotated to highlight example lengths and angles that satisfy inter- and intrabody design requirements.

Fig. 2

Flowchart of an exhaustive search algorithm for generating a single, valid DRF. An example run within $d_{\min }=52\mathrm{mm}$ and $d_{\max }=100\mathrm{mm}$ yielded $\sim 750,000$ individual valid designs.

Fig. 3

Flowchart of an algorithm for forming groups of mutually compatible tools designs from the exhaustive search toolList resulting from Fig. 2. In the current work, 10 such groups were formed (denoted A, B, …, K), each containing 6 to 10 mutually compatible DRFs.

Fig. 4

Example DRF generated using the algorithm described in Fig. 2. CAD models were exported as STL files ready for 3-D printing. The models included posts for attachment of retroreflective markers at locations corresponding to $d_1,\dots ,d_6$ as well as features such as posts, an X-shaped support frame; pass-through holes for attaching a pointer with set screws; and a name designator (e.g., APPLE-2 for group A, tool 2).

Fig. 5

Experimental setup. (a) Pivot calibration tool. The distance from the DRF origin to the pointer tip was fixed at 53 mm for all tools, with each DRF attached to the pointer via the central clearance hole. (b) Illustration of the experimental setup for validation of DRF designs. A computer-controlled motion system on an optical bench was used in combination with NDI trackers and a selection of test objects for pivot calibration (steel divot), FRE measurements (grid points via computer-controlled motion stages), and TRE measurements (a CT head phantom mimicking anatomy of the skull).

Fig. 6

Open-source library of DRFs. (left) Photograph of the A (“Apple”) group comprising 10 mutually compatible tools produced on a 3-D printer and outfitted with NDI retroreflective markers. The hole pattern in the background marks 1 in. (2.54 cm) scale. (right) Illustration of CAD renderings for the 10 groups, denoted A–K.

Fig. 7

Distribution of intertool distances within a group, where each DRF is represented as a point in 6-D space.

Fig. 8

Illustration of simultaneous multiple tool tracking (six tools from the A group) using an NDI Polaris Vicra. A colored circle is superimposed on the photograph to identify the six tools evident in NDI Track.

Fig. 9

Experimental validation of DRF designs. Measurements are shown for the 10 DRFs in group A. (a) Pivot calibration error. (b) FRE. (c) TRE. The dashed horizontal line marks the average median value of the custom DRFs.