A comparison of registration techniques for computer- and image-assisted elbow surgery

Abstract

Optimal function following elbow replacement surgery is dependent on the accurate replication of the elbow's flexion-extension axis. Currently, position and orientation of the axis are estimated from visual landmarks. In order to develop computer-assisted techniques to more accurately define this axis, a surface-based registration technique employing a hand-held laser scanner was evaluated against a conventional paired-point registration method to determine whether it produced improved alignment of the flexion-extension axis of the elbow. Registration error was 0.8 ± 0.3 mm for surface-based registration, compared with 1.9 ± 1.0 mm for the conventional registration method. These results suggest that the implementation of a surface-based registration technique may lead to a more accurate axis determination and improved clinical outcomes following elbow replacement surgery.

• Surface-based registration
• elbow replacement
• computer-assisted surgery

Introduction

Fracture or non-union of the distal humerus, bone loss due to tumors, or destruction of the elbow joint caused by arthritis are the most common indications for implantation of a total elbow prosthesis [1]. In elbow replacement surgery, optimal post-operative function is dependant on the accurate replication of the flexion-extension axis, defined by the geometric centers of the capitellum and trochlear sulcus [2–5]. Intra-operatively, correct implant alignment relies on a visual estimation of anatomic landmarks to locate this axis [6]. Malalignment may lead to early aseptic loosening and may be an important cause for revision surgery [7]. With respect to axis determination, no computer-assisted techniques have yet been reported for use in elbow replacement surgery. As a potential solution, image-guided techniques may be implemented.

Image-guided surgery employs pre-operatively acquired images as a means of guiding an instrument towards a target during surgery. Computed tomography (CT) is a valuable tool for pre-operative assessment as it accurately represents the actual geometry of the anatomy in question [8]. The accuracy with which the target may be identified depends on the registration approach employed. In computer-assisted orthopaedic surgery, approaches employing both point-based and surface-based registration techniques are emerging. These techniques have led to significant improvements in the accuracy and reproducibility of implant positioning and fracture fixation at other joints [9–15]. However, while many of these approaches have been directed at the spine, hip and knee, application of registration techniques to the upper limb has so far been done primarily to facilitate the analysis of kinematics [16], [17] and pre-operative work-up [18].

In view of the foregoing, the purpose of this study was to determine whether a surface-based registration technique, employing a hand-held laser scanner, would lead to improved alignment of the flexion-extension axis of the elbow. Our hypothesis was that the accuracy of the laser scanner in collecting surface data, combined with a surface-based registration approach, would contribute to a more accurate axis alignment.

Materials and methods

Image acquisition and processing

Twelve fresh-frozen cadaveric distal humeri (nine left, three right) were selected for registration. Volumetric CT images (approximately 50 slices along the distal portion of the humerus with 0.3 × 0.3 × 0.625 mm voxels) of each specimen were obtained using a helical CT scanner (GE LightSpeed Ultra, New Berlin, WI). The field of view (FOV) was 16 × 16 cm with a 512 × 512 reconstruction matrix. A surface model of each specimen was reconstructed from acquired CT images using a modified version of the Marching Cubes algorithm within the Visualization ToolKit (VTK) [19].

Tracking modalities

Two devices were used to acquire data from each specimen (for registration to the CT dataset). The first was a tracked probe instrumented with a receiver from an electromagnetic tracking device (Flock of Birds, Ascension Technology Corporation, Burlington, VT). As the digitizing probe tip traced the surface of the bone, points in space relative to a transmitter were recorded (the tracked probe had an accuracy of 1.8 mm RMS for position and 0.5° for orientation). Geometric centers were then calculated and 3D surface models were generated from these point clouds. The second device was a hand-held laser scanner (FastSCAN™ Cobra, Polhemus, Inc., Colchester, VT). This consisted of a hand-held wand with an attached camera that recorded the projected profile of an emitted fan-beam laser. As the laser was swept across the surface, a point cloud corresponding to surface samples was plotted on a computer monitor in real time and a 3D surface model was generated (Figure 1). Using the laser scanner, up to 5,000 points were collected over a short scanning period, with approximately three times as many points being collected than when using the tracked probe. The hand-held wand was equipped with a magnetic tracker and had an accuracy of 1.0 mm RMS for position and 1.0° for orientation.

Figure 1. (a) The FastSCAN™ wand with transmitter. (b) The wand is swept over an object when performing a scan in a manner analogous to spray painting. (c) While scanning, a real-time point cloud or (in this case) surface representation is shown on a computer display to enable the user to see what has been scanned. Here, only the articular surface has been scanned, as this is what will be registered to the CT dataset.

Registration

Three different registration procedures – one paired-point (PP) and two surface-based (tracked probe employing surface and hand-held laser scanner employing registration – were performed on each specimen.

To perform PP registration, key anatomical landmarks (the capitellum, trochlear sulcus, proximal humeral shaft and distal humeral shaft) were digitized using the tracked probe. Using the geometric centers of these landmarks (Figure 2), PP registration of the specimen to the CT dataset was performed using Horn's closed form solution [20], thereby obtaining the rigid transformation of the two sets of points.

Figure 2. A visualization of the four digitized landmarks fitted to simple geometries. [Color version available online.]

Alternatively, surface-based registration involved selecting a cloud of points on the surface of the target anatomy. This point cloud was then registered to the CT dataset using the iterative closest point (ICP) algorithm [21]. Data from both the tracked probe (TP) and the hand-held laser scanner (HHLS) were used in the surface-based registration. For the tracked probe, the articular surface was digitized and a surface model was computed using the commercially available FastRBF Toolbox® (FarField Technology Ltd., Christchurch, New Zealand) interfaced to MATLAB® (The MathWorks, Inc., Natick, MA). From this surface model, registration to the CT dataset (TP-ICP) could be performed. The surfaces computed from the tracked probe point clouds appeared noisy and did not closely resemble the actual specimen. Consequently, the resulting registration was very poor. To improve the registration, a spline smoothing algorithm was applied to smooth out the surface [22]. The spline smoothing algorithm pulls the surface near the data points, but does not force it to pass through all of them. For the hand-held laser scanner, each point cloud generated was also processed by FastRBF to compute a surface model, and registration to the CT dataset (HHLS-ICP) was subsequently performed.

Variables and statistical analyses

Surface acquisition was performed once (for each tracking modality), while the process of registration was repeated five times. Statistical analysis was performed to examine differences in registration accuracy with respect to the three techniques being evaluated. A Student's t-test was used to compare the results for the conventional registration with those for the surface-based registration. Differences between the three groups were then analyzed with an ANOVA to ascertain whether the means of the independent distributions were significantly different. Both the ANOVA and Student's t-test were performed at the α = 0.05 level of significance.

Results

Registration error was lowest for the HHLS-ICP registration method, with an RMS error of 0.8 ± 0.3 mm in translation. This result compared with an RMS error of 1.5 ± 0.5 mm for the TP-ICP registration and 1.9 ± 1.0 mm for the PP registration (Table I, Figure 3). The HHLS-ICP method also produced the most consistent results. The maximum inaccuracy of the registration in translation was 1.4 mm for the HHLS-ICP registration, compared with 2.4 mm for TP-ICP registration and 4.4 mm for PP registration. All results were statistically significant (α < 0.001).

Figure 3. Mean RMS registration error (+1 SD) for the three registration techniques evaluated (in mm). The implementation of the surface-based registration produced not only improved registration accuracy, but also a more consistent result, as evidenced by the smaller standard deviation shown on the bars at far right. The HHLS-ICP method was the most accurate and consistent of the three techniques.

Table I.  RMS target registration error: translation (SD in parentheses).

Specimen	PP registration (mm)	TP-ICP registration (mm)	HHLS-ICP registration (mm)
1	2.3 (0.9)	1.1 (0.1)	1.0 (0.2)
2	3.1 (1.5)	0.9 (0.2)	0.5 (0.1)
3	2.5 (1.0)	1.5 (0.1)	0.8 (0.1)
4	1.4 (0.5)	1.0 (0.2)	0.8 (0.2)
5	1.3 (0.5)	1.4 (0.1)	0.4 (0.1)
6	1.9 (0.6)	2.0 (0.3)	0.8 (0.1)
7	0.9 (0.5)	2.3 (0.1)	1.1 (0.3)
8	1.2 (0.6)	1.7 (0.1)	0.4 (0.1)
9	2.9 (0.8)	1.3 (0.1)	0.4 (0.1)
10	1.1 (0.3)	1.2 (0.3)	1.0 (0.1)
11	1.6 (0.2)	1.6 (0.3)	0.5 (0.2)
12	1.6 (1.1)	1.0 (0.2)	1.0 (0.4)

The source (digitized) flexion-extension axis following registration was compared against the flexion-extension axis of the target landmarks (Figure 4). Errors in PP registration were most apparent in the coronal plane, while TP-ICP registration often resulted in an error along the transverse plane. In the case of the TP-ICP registration, there was a significant anterior translation of the flexion-extension axis, compared with either a superior or inferior translation following PP registration. While errors tended towards an anterior translation for the HHLS-ICP registration, this trend was not statistically significant like it was with the other two techniques (Table II).

Figure 4. Internal-external (top) and varus-valgus (bottom) mean (dashed line) and maximum (dotted line) error in the flexion-extension axis determination for three methods (PP – left; TP-ICP – center; and HHLS-ICP – right). The solid line represents the target flexion-extension axis. All units are in mm. [Color version available online.]

Table II.  Directional shift in the flexion-extension axis. A shift in the positive x-direction represents a shift in the anterior direction; a shift in the positive y-direction represents a shift in the superior direction; and a shift in the positive z-direction represents a shift in the medial direction.

	PP registration			TP-ICP registration			HHLS-ICP registration
	X	Y	Z	X	Y	Z	X	Y	Z
Specimen	(+)	(+)	(+)	(+)	(+)	(+)	(+)	(+)	(+)
1	−0.4	2.1	0.2	1.0	0.1	−0.1	0.9	−0.2	0.0
2	0.1	2.9	0.1	−2.1	0.1	0.1	−0.1	−0.1	0.2
3	−0.5	2.3	0.5	1.2	0.5	0.7	−0.2	−0.2	0.3
4	0.3	−1.1	−0.1	0.9	0.2	−0.1	1.0	0.3	0.0
5	0.3	−1.0	−0.1	1.4	0.0	0.0	0.7	−0.3	−0.1
6	0.3	−1.6	−0.2	1.8	−0.2	−0.1	0.9	−0.2	0.2
7	0.1	0.1	0.0	2.2	−0.1	0.1	0.9	0.2	0.1
8	0.1	−0.9	−0.1	1.3	0.1	0.3	0.1	−0.1	−0.1
9	0.5	−2.4	−0.3	1.8	0.0	0.4	0.2	0.2	−0.2
10	0.0	0.6	0.0	0.6	0.6	0.0	0.2	0.4	−0.6
11	0.3	1.4	−0.2	−0.9	0.2	−0.7	0.2	−0.3	0.1
12	0.2	−0.3	−0.4	−1.6	0.0	0.0	−0.4	0.4	0.2
Mean	0.1	0.2	−0.1	0.6	0.1	0.1	0.4	0.0	0.0
SD	0.3	1.7	0.2	1.4	0.2	0.3	0.5	0.3	0.3
Maximum	0.5	2.9	0.5	2.2	0.6	0.7	1.0	0.4	0.6

Discussion

The accurate alignment of a prosthesis is an important variable for a successful clinical outcome following joint replacement surgery [1], [2], [6], [13]. With respect to the elbow, correct selection of the flexion-extension axis allows for proper placement of the implant, thereby recreating normal biomechanics, including natural joint motion and muscle moment arms about the elbow[1], [2], [6]. While the geometric centers of the trochlear sulcus and capitellum define the flexion-extension axis, locating these landmarks is difficult since they are not visible and must be estimated from external structures. This study focussed on the effectiveness of the type of registration implemented and the method used to acquire data from the physical specimen in order to perform registration.

We found surface-based registration to be more accurate than anatomical PP registration, with HHLS-ICP registration yielding the highest accuracy and repeatability (α < 0.001). HHLS-ICP registration led to a more consistent and accurate alignment of the source flexion-extension axis to the target flexion-extension axis, as evidenced by the small deviation shown in Figure 4.

A study by Marmulla et al. [23] found laser-scanner-based registration to be superior to other fiducial-less approaches for cranial computer-assisted surgery. However, this study was not comparative as the authors referenced the results of other fiducial-less approaches and did not obtain the results themselves. Currently, there are no known studies that directly compare laser-scanner-based registration techniques with other fiducial-less approaches in computer-assisted orthopaedic surgery.

Varus-valgus error (a medial or lateral tilt of the flexion-extension axis in the coronal plane) was most prominent for the PP registration technique, which was found to have the largest error and variation compared to surface-based registration. This may have been due to the errors in identifying the homologous landmark pairs on the specimen and on the CT dataset. When performing PP registration using anatomical landmarks, accuracy is dependent on the correct identification of the landmark by the user. In this study, the interpretation of which surface area constitutes the capitellum and trochlear sulcus is not always apparent. This may become even more evident when interpreting landmarks on the physical anatomy and then on a computer surface model. If the calculated landmarks are subject to variation based on user perspective, so too is the resulting registration. In addition, error can also be attributed to the requirement for two digitized arcs along the humeral shaft in order to perform registration. This is prone to variation as the exact replication of each arc is difficult to achieve.

A more accurate alternative to PP registration using anatomical landmarks is the use of external markers. This involves attaching a minimum of three fiducial markers to the patient prior to the acquisition of the pre-operative image. During surgery, the fiducial markers on the patient are registered to the markers in the pre-operative image. Past studies have shown surface-based registration to be less accurate than paired-point registration incorporating the use of fiducial markers[12], [13], [20]. However, this procedure is more invasive as it requires the implantation of markers in bone; merely attaching fiducial markers to the patient's skin results in additional erro [1], [24]. In some cases, the anatomical landmarks of the bone are destroyed due to fractures and diseases such as rheumatoid arthritis, in which case registration of the target anatomy to a reflection of the CT scan of the contralateral side may be more ideal. Fiducial markers cannot be used in this situation. In the case of a distal humeral fracture, small bone fragments cannot be registered to the pre-operative image using fiducial markers as they may move between image acquisition and surgery. However, by registering each fragment to the pre-operative image using a surface-based approach, they can then be tracked and properly aligned.

The surface models generated by the laser scanner were a close representation of the actual specimen, and measurements of the laser-scanned surface model and the CT surface model were very similar. As depicted in Figure 1, the registration will have greater success if only the articular surface is scanned and not any of the soft tissues. In the case of the elbow, this is not a problem since the articular surface of the distal humerus is entirely exposed. Two acknowledged problems with ICP-like algorithms are the requirement for a good initial estimate and the minimization of statistical outliers [11]. As in our study, others have applied a similar paired-point registration as a coarse alignment and have achieved accurate results [12], [25]. To address the second issue, the software used for generating the surface model successfully removes isolated points that lie far from the actual surface. Thus, there were no statistical outliers present in the dataset.

TP-ICP registration resulted in a consistent registration error, but is not as accurate as the HHLS-ICP registration. This may have resulted from the method of surface acquisition. The surface model generated from the tracked probe digitization included a noise signal that necessitated the application of a spline smoothing algorithm. This noise was probably inherent in the magnetic tracker and may have also been user-induced. Rough bony structures made the digitization process somewhat difficult and may have contributed to the additional noise present in the data. Prior to applying the algorithm, the noise caused significant error in the registration. However, even though the application of the spline smoothing reduced this error, excessive detail was removed from the surface, preventing registration accuracy from approaching that of the HHLS-ICP method. To establish a surface model, the entire articular surface of the distal humerus was digitized. While some studies have used several hundred surface points for performing the registration [15], recent work suggests an accurate surface registration can be achieved simply by selecting 7–30 well-spaced points on the surface [10], [11], [13–15]. Selecting a small number of points distributed across the surface decreases the likelihood of overlapping points that may have led to greater error in the generation of a surface model.

Internal-external error (a medial or lateral tilt of the flexion-extension axis in the transverse plane) was most prominent for TP-ICP registration. The source flexion-extension axis appeared to be shifted away from the target flexion-extension axis anteriorly, as shown in Figure 4b. This can be explained by the difference between the two surfaces being registered together. Unlike the surface model produced by the laser scanner, there appeared to be a small difference in measurements between the tracked probe surface model and the CT surface model. The radius of curvature for both the capitellum and trochlear sulcus was greater for the CT surface model. When performing the coarse alignment, the centers of the two landmarks are aligned with one another. If the two surfaces being registered are not the same, their alignment during surface-based registration will create a displacement between the source landmarks and target landmarks. In this case, the shift was generally in the anterior direction.

Surface acquisition was faster for the hand-held laser scanner, taking approximately 10-15 seconds to acquire data from the articular surface of the distal humerus. The selection of paired points and computation of the transformation matrix for PP registration took approximately 3 minutes. Computation of the ICP algorithm required an additional 30 seconds.

While the use of the hand-held laser scanner led to an accurate registration with the CT dataset, it was only employed by one user. However, when the hand-held laser scanner was evaluated on five novice users outside of this study using simple geometric shapes, the system demonstrated a high degree of intra- and inter-user repeatability. Another issue that needs to be addressed is the presence of liquid in the scanning environment. Surfaces may be difficult to scan in the presence of small pools of blood, as these may cause the surface to become visually hindered or create significant laser refraction. A potential deficiency of the hand-held laser scanner concerns its ability to acquire surface data from translucent or highly reflective surfaces. In these cases, the laser beam is deflected, creating an increase in the amount of noise present in the resulting scan. To correct this error, the laser needs to be pointed directly onto the surface and not at an angle. Fortunately, scanning the articular surface of the distal humerus did not lead to this problem in the in-vitro environment; however, further refinement may be needed prior to clinical implementation. A concern regarding computer-assisted joint replacement is the limited exposure of the joint intra-operatively. However, in most clinical cases, the majority of the articular surface will be available to the surgeon. Thus, while this study was conducted in a simulated in-vitro environment, we anticipate that the same registration accuracy may be found in the presence of surrounding tissues.

In conclusion, the high reliability of the surface-based registration combined with the implementation of the hand-held laser scanner show promise for providing the surgeon with a valuable clinical tool in the future. A reliable surface-based registration technique will lead to a more accurate determination of the flexion-extension axis of the elbow, allowing for proper placement not only of implants, but also of articulated external fixators and ligament reconstructions. This may well improve clinical outcomes following elbow replacement surgery, as successfully targeting the flexion-extension axis is expected to lead to improved joint motion. Moreover, similar applications may be efficacious for other joints.