Implementation of a semiautomatic method to design patient-specific instruments for corrective osteotomy of the radius

As a standard CAD software for PSI design, we evaluated 3-matic (Materialise, Leuven, Belgium), an established PSI design software package already adopted in many clinical studies [23, 24]. In this software, several manual operations are required to accomplish the task of designing PSIs for corrective osteotomy. The adopted workflow is summarized in Fig. 2a. We started the design of the implant by importing the STL datasets of the proximal and the distal bone polygons in the planned relative position. The sweep-loft function was then used to interpolate in-between these virtual bone segments. “Push and pull” manual operations were then required to locally smooth the interpolated region. On the surface of this corrected bone model, we manually positioned and oriented lines representing drill trajectories. A 2D sketch of the implant footprint was manually drawn and projected onto the corrected bone surface to select the implant footprint including the screw locations. The footprint was extruded, and the edges were smoothed. Finally, drill holes were created by subtracting cylinders of a specified diameter at locations indicated by the drill lines.

In order to create the surgical guide, the repositioned distal segment had to be registered to the original position (via point-cloud fitting). This enabled retrieving the transformation parameters (which, in this case, could not be provided via the transformation matrix) to bring the distal drilling lines to the affected state of the bone. After importing the STL of the affected bone, a 2D sketch, including the drilling line insertion points, was drawn onto its surface to select the guide footprint. The same steps mentioned before were then executed onto the guide footprint. Finally, a slit of thickness 0.8 mm was created centered around the previously chosen cutting plane.

A partially customized CAD software solution was developed with Siemens NX (formerly known as NX Unigraphics; Siemens PLM software, Plano, TX, USA). Siemens NX is a multi-purpose industrial design, simulation and manufacturing software providing a collection of Parametric Product Models under the name “Product Template Studio.” Every Parametric Product Model corresponds to a function that can be manually activated in NX. In “Product Template Studio,” the user can create, by Visual Programming, custom interfaces by linking different Parametric Product Models to automatize the design. In this environment, we created two separate applications, respectively, for the implant and guide design. The overall workflow of implant and guide design applications are summarized in Fig. 2b and detailed below.

Implant design application A local coordinate system (LCS) has to be defined for both the distal and proximal bone parts. These LCSs will be used to position and project two predefined 2D implant sketches adequately onto the repositioned bone model (Fig. 3a). The 2D sketches can then be manually adjusted by dragging predefined vertices.

After the sketches have been shaped as desired, the automatic design procedure is started. In brief, both proximal and distal sketches are projected onto the target bone to retrieve two partial implant footprints. The partial footprints are then extruded and merged by interpolation to create the plate (Fig. 3b). Corners around the plate are blended to avoid sharp edges. To finish implant design, screw holes were created centered around the predefined drilling lines.

Guide design application The application for surgical guide design uses almost the same consecutive commands as described for the implant design. However, the interpolation step is not required for the surgical guide design. The local coordinate system (LCS) is defined onto the surface of the affected bone polygon. Again, a predefined 2D sketch for the guide is positioned at the origin of the LCSs. After manual optimization of the 2D sketch, the automatic design procedure is started with the same steps as previously mentioned. The cutting slit is manually created by using the cutting plane position. To realize the correct positions for the drilling holes on the surgical guide, the inverse of the correction matrix (M _c ⁻¹ ) is used to transform (a copy of) the distal lines representing the distal drilling lines, on the correct positions with respect to the surgical guide. The slit of thickness 0.8 mm was created centered around the predefined cutting plane.

A semiautomatic CAD wizard was added to the existing custom software for surgical planning [21, 22]. The wizard was implemented in the C++ programming language (Visual Studio 2013, Microsoft, Redmond, WA). The Visualization Toolkit (VTK 7.0.0) was used for modeling and visualization in 3D space. Sequential steps in the design approaches are summarized in the workflow of Fig. 2c.

Drill-line placement A virtual model of the osteotomized bone segments in the planned position is created by application of the correction matrix \( M_{\text{c}} \) (Fig. 4a). The user selects a number \( n \) of screw insertion points by tagging them on this model. Screw trajectories represented by lines are automatically proposed in the direction of the local surface normal of the bone model although the line can be adjusted manually (Fig. 4b).

Corrected bone model In order to shape the implant footprint, i.e., the portion of the implant fitting the bone surface, a model of the corrected bone without a bone defect is realized by interpolating the space between the repositioned segments. Interpolation is done by sweeping the bone cross section along a cubic Bezier curve with starting and ending control points, respectively, at the centroid of the cross section in the proximal and distal bone segments [9].

Footprint surface selection To automatically position the box for selecting an initial footprint out of the affected bone polygon, the principal axes of inertia of the selected set of screw insertion points are calculated as the eigenvectors of their Inertia Tensor. They define a local coordinate system in which a virtual box is positioned that bounds the screw entry points. The box (Fig. 4c) is enlarged in the extrusion direction by h, which is equal to the distance between the centroid of the screw entry points and the centroid of points where they exit the bone. In the remaining directions, the box is enlarged by a user-defined size w, to leave space between the screws and the border of the plate. In this study, w was 6 mm. The center of the box is positioned in the centroid of the screw entry points. The box can be resized by the user. A regular grid of points is then projected from the volar side of the box toward the corrected bone polygon along the average screw direction (\( \vec{d} \)) (Fig. 4d). The result of the projection is a grid of 3D points equally spaced in two out of three dimensions. Tessellation of the projected points results in an initial implant footprint or inner surface, i.e., the portion of the bone surface to which the implant fits.

After selecting the footprint surface, the general idea is to copy and translate the footprint in the extrusion direction and then create a smooth circumferential rim by connecting each boundary point (\( p_{i} \)) of the inner surface to its corresponding point (\( p_{i} '' \)) on the outer surface by means of a cubic b-spline. Each b-spline \( b_{i} \) (with \( i = 1 \ldots n \) and \( n \) being the number of points on the outline of the inner and outer plate surfaces) is interpolating \( p_{i} \), \( p''_{ i} \) and an intermediate point \( p'_{i} \) (Fig. 5b).

The position of the intermediate point \( p'_{i} \) determines the orientation of the plane in which the b-spline resides and the bulge of the circumferential rim. Initially, the position of \( p'_{i} \) iswhere \( b \) and \( t \) are user-defined scalars representing the bulge of the implant and the implant thickness; \( \vec{e} \) is a bisecting unity vector starting at \( p_{i} \) splitting the external counterclockwise angle (α) between the vectors \( \overrightarrow {{p_{i} p_{{\left( {i - 1} \right)}} }} \) and \( \overrightarrow {{p_{i} p_{{\left( {i + 1} \right)}} }} \) in two (Fig. 5c).

However, design of circumferential rims in the procedure above may not work in case the outline is locally strongly concave, i.e., \( \alpha_{i} < \) 180° in which case intersections of b-splines can occur depending on the edge bulge b (see Fig. 5c).

Therefore, we implemented an iterative algorithm that, for a user-defined value of \( b \), checks for b-spline intersections and reduces concavity by smoothing the footprint outline, until the b-splines no longer intersect. Finding intersections between each couple of segments was implemented as described in [25]. Whenever an intersection is found, we applied a simple central moving average filter to the outline points, which has the effect of repositioning each point based on the position of its two boundary neighbors. Based on the new position of the points \( p_{i} \), points \( p'_{i} \) are recalculated and intersections are checked. This procedure is iterated until no more intersections are found. Since the b-splines that define the circumferential rim do not depend on where along the projection axis (\( \vec{d} \)) each point \( p_{i} \) is found, smoothing of the plate outline is implemented in 2D. The 2D smoothed contour is then reprojected onto the bone model, and the surface of the bone contained inside the 3D contour is selected as the new implant footprint.

Outer surface smoothing A copy of the inner surface is smoothed and translated over a distance equal to the implant thickness \( t \) (default 2.4 mm) in the direction (\( \vec{d} \)) and represents the top surface of the plate. Smoothing of the top surface is accomplished by Laplacian smoothing (15 iterations) [26, 27]; the new position of each interior mesh points \( q_{i} \) after smoothing is calculated aswith \( N_{i} \) being the set of the connected neighboring points to \( q_{i} \) and \( \lambda = 0.3 \) being the relaxation factor.

Surgical guide modeling Once the design of the implant is completed, the guide design is subsequently started. The first step in the guide modeling is transforming the drilling holes (that are already defined in the plate design method) back to the affected bone model through the inverse of the correction matrix \( M_{\text{c}}^{ - 1} \). We use the same methodology described before for automatically sizing a virtual box and selecting the bone surface for fitting the guide based on the screw insertion points, to select the surface of the affected bone where the cutting guide will be positioned. This time, the selecting box is slightly oversized to better enclose the bone, which ensures a better fit and easier guide positioning during surgery [15]. The selected guide footprint is directly extruded, and a cutting slit and screw holes are included into the guide by Boolean subtraction.

A laboratory experiment was performed to evaluate the feasibility to print the PSI designed with the novel method and to use it for bone repositioning. 3D models of an affected bone, the corresponding PSIs and the corrected model (reference model) were 3D printed in Polycarbonate-ISO (PC-ISO) (Fig. 6). Printing was performed with a Fortus 450 mc fused deposition modeling printer (Stratasys, Eden, Minnesota, USA). Accuracy of the printer was ± 0.127 mm in all the printing directions. A mock surgery was performed via the guide and the implant, as previously described in [9], onto the plastic model. CT images of the corrected bone and of the reference model were then acquired. The achieved alignment was finally compared to the reference model as described in the previous section by segmentation and registration of the distal and proximal bone segments. Residual positioning errors were expressed in 6 DoF.

Three biomedical engineers were recruited, each with experience in implant design with one of the three considered design methods. Preoperative virtual 3D plans of five patients were selected that were previously treated at our institute for corrective osteotomy using a patient-specific implant. Preoperative plans were provided to the participating engineers (STL models of bone segments, the cutting plane and the correction matrix \( M_{\text{C}} \)). Approximate screw positions and drilling line orientations were provided to the participants, via 2D sketches. This simulated the actual qualitative transfer of information between surgeons and engineers in the design stage. For every patient case, the engineers were asked to design a patient-specific volar radius plate and its companion surgical guide featuring the cutting slit and the drill holes required for plate positioning. Since PSI design is often an iterative process, due to modifications requested by the surgeon and/or recommended after strength calculations using finite element analysis, after completing the design task, the engineers were asked to modify the screw configuration of the osteosynthesis material.

Measurements In each procedure, design time, the number of mouse movements and the number of keyboard strokes were recorded from the beginning until the end of the design process through Recorder User Input (RUI) [28], a publicly available logging tool. Tracked mouse movements were also converted into a single image using IOGraph (IOGraph V1.0.1, © Anatoly Zenkov & Andrey Shipilov, 2010–2018), which enabled illustration of the complexity of the design task in a graphical fashion. To check if the activity level of the different users during the tasks was comparable, we also calculated the mouse velocity and the number of clicks and strokes per minute of activity. The validity of all the designed PSI shapes was preliminary assessed by an experienced hand surgeon (SDS).