Development of a fluoroscopically guided robotic assistant for instrument placement in pelvic trauma surgery

Abstract.

Purpose: A method for fluoroscopic guidance of a robotic assistant is presented for instrument placement in pelvic trauma surgery. The solution uses fluoroscopic images acquired in standard clinical workflow and helps avoid repeat fluoroscopy commonly performed during implant guidance.

Approach: Images acquired from a mobile C-arm are used to perform 3D–2D registration of both the patient (via patient CT) and the robot (via CAD model of a surgical instrument attached to its end effector, e.g; a drill guide), guiding the robot to target trajectories defined in the patient CT. The proposed approach avoids C-arm gantry motion, instead manipulating the robot to acquire disparate views of the instrument. Phantom and cadaver studies were performed to determine operating parameters and assess the accuracy of the proposed approach in aligning a standard drill guide instrument.

Results: The proposed approach achieved average drill guide tip placement accuracy of $1.57\pm 0.47\mathrm{mm}$ and angular alignment of $0.35\pm 0.32\mathrm{deg}$ in phantom studies. The errors remained within 2 mm and 1 deg in cadaver experiments, comparable to the margins of errors provided by surgical trackers (but operating without the need for external tracking).

Conclusions: By operating at a fixed fluoroscopic perspective and eliminating the need for encoded C-arm gantry movement, the proposed approach simplifies and expedites the registration of image-guided robotic assistants and can be used with simple, non-calibrated, non-encoded, and non-isocentric C-arm systems to accurately guide a robotic device in a manner that is compatible with the surgical workflow.

1. Introduction

Surgical treatment of pelvic fractures following traumatic injury involves fixation of anatomy using Kirschner wires (K-wires) and cannulated screws to join fractured fragments and promote bone healing (viz. osteosynthesis). Implant placement is challenging due to the complexity of pelvic anatomy, which consists of narrow bone corridors—for example, as long as 104 mm and as small as 7-mm width in the pubic ramus.¹ There is also low tolerance for cortical breach of delivered implants due to proximity to viscera and critical vasculature.² Misalignment of a K-wire by as little as 4 deg can result in clinically significant cortical breach in certain corridors such as the iliosacral joint.³ Improper fixation can lead to poor long-term functional outcomes, including nonstructural scoliosis, lumbar/sacroiliac pain, and abnormal gait.⁴

Intraoperative fluoroscopy is commonly used to assist the surgeon during pelvic fracture fixation, providing visualization of surgical devices and the patient anatomy. Estimating the 3D pose of surgical devices with respect to the superimposed anatomy in the 2D fluoroscopic projection, however, is challenging, error prone, and requires long learning curves for orthopaedic surgeons to master.⁵ Surgeons often resort to “trial-and-error” to repeatedly retract and reinsert the K-wire to ensure it is on an appropriate trajectory. This manual, qualitative process also necessitates standardized fluoroscopic views to better reckon the 3D pose of the surgical device with respect to the pelvis. The term “fluoro-hunting” refers to repeat imaging to align the imaging system with the desired view.⁶ The combination of trial-and-error and fluoro-hunting not only impacts surgical workflow by increasing the operation time, but also increases radiation dose to both the patient and the surgeon.^7,8 Current fluoroscopy exposure times for K-wire and screw placement can range from 2 to 18 min.^5,9

Robotic assistance can improve the accuracy and safety of procedures such as pelvic fracture fixation,^10–12 reduce trial and error in implant placement, and reduce radiation dose associated with fluoro hunting. Several robotic systems have been reported for assistance of drilling or bone resection, such as the Navio Precision Freehand Sculptor (Smith & Nephew, London) for knee and patellofemoral arthroplasty with virtual constraints and motor speed control to avoid inadvertent bone removal.^13,14 The system operates according to a virtual model of patient anatomy based on landmark features without preoperative CT. In pelvic trauma surgery, especially in percutaneous procedures, it is difficult to expose enough cortical bone surface for such landmark-based guidance.

Other robots operate according to tracking in intraoperative cone-beam CT (CBCT) and/or stereotactic laser guides to register with preoperative CT—for example, the ROSA robot (Zimmer Biomet, Warsaw, Indiana) for intracranial biopsy, endoscopy, and electrode placement¹⁵ and the ExcelsiusGPS robot (Globus Medical, Inc., Audubon, Pennsylvania) for drill guide alignment in spinal pedicle screw placement.¹⁶ The Mako robot (Stryker, Kalamazoo, Michigan) is affixed to bone anatomy to assist with sawing and milling in knee and hip replacements, and the system reported by Dagnino et al.¹⁷ uses a robot attached to bone fragments to perform fracture reduction. The system by Westphal et al.¹⁸ uses a two-finger gripper to secure and align bone fragments guided by intraoperative CBCT.¹⁹ Systems for fracture fixation include the TiRobot (TINAVI Medical Technologies, China), which uses a structured arm to align a drill sleeve for screw trajectories in femoral neck fractures. Systems that rely on optical tracking require unobstructed line-of-sight between markers and the camera, introducing interruption to workflow in scenarios with a large, complex patient setup, and a broad diversity of device trajectories, such as pelvic trauma surgery.^20–22 Intraoperative CBCT alone costs time and dose to update the patient registration and can suffer from a limited field-of-view. Consequently, robotic systems that rely on optical trackers and intraoperative CBCT have seen limited adoption in orthopaedic trauma surgery.^20,23

This work details an image-guided robotic system that is navigated using registration of fluoroscopic views normally acquired during the procedure, thus, mitigating the workflow challenges of tracker-based solutions. The approach makes use of the fluoroscopic imaging device that is already present in the OR and absolves the need for trial-and-error and fluoro-hunting. The system operates by: (1) registering the patient preoperative CT to the imaging system; (2) registering the robot to the imaging system; and (3) driving the robot to a trajectory defined in the CT. Previous work presented a workflow that uses fluoroscopic projections acquired at multiple poses of a C-arm imaging system to capture multiple views of the patient and robot, followed by 3D–2D “known-component” registration of the patient CT and 3D instrument CAD model to the projections.^24–26 This workflow, referred to here as a “rotating-gantry” workflow, requires use of an encoded, geometrically calibrated C-arm to relate imaging system geometry between acquired views.

A novel robotic workflow for fluoroscopically guided orthopaedic procedures is presented. In the proposed workflow, the C-arm gantry remains at a single pose, and multiple projections are acquired of the robotically held instrument and patient as the robot performs small rotations of the instrument over the patient. The “fixed-gantry” workflow reduces dependencies on encoded, geometrically calibrated C-arms and helps mitigate the challenges associated with the motion of C-arm gantries (especially non-isocentric)—including the challenges of acquiring views that keep the patient and robot within the FOV and moving the device in proximity to surgical setup. The approach was evaluated in phantom, and an analysis of operating parameters was performed. The phantom study additionally compared the novel fixed-gantry workflow to the rotating gantry workflow in the context of pelvic fracture fixation. The operating parameters determined in this study were then translated to pre-clinical studies in a cadaver specimen to assess performance in a realistic operating setting.

2. Methods

2.1. Overview of Robotic Instrument Placement

The proposed approach for fluoroscopically guided robotic instrument placement (Fig. 1) uses radiographs acquired from a mobile C-arm that captures both the anatomy and the robotically held instrument. Computed registrations resolve the pose of the patient (via their preoperative CT) and the robot (via instrument CAD model and robot kinematics) such that the instrument can be aligned with target planned trajectories defined in CT. This alignment is solved for using Eq. (1), summarized below, and further detailed in the sections that follow (Table 1).

$${\hat{T}}_{\text{base}}^{\text{end}}=\underset{\text{Robot}}{\underbrace{T_{\text{base}}^{\text{end}}{T}_{\text{end}}^{\mathrm{inst}}}}\underset{\text{Registration}}{\underbrace{{(T_{\mathrm{wrld}}^{\mathrm{inst}})}^{-1}{T}_{\mathrm{wrld}}^{\mathrm{ct}}}}\underset{\text{Plan}}{\underbrace{T_{\mathrm{ct}}^{\text{plan}}{T}_{\text{plan}}^{\mathrm{inst}}}}{(T_{\text{end}}^{\mathrm{inst}})}^{-1}.$$ (1)

Fig. 1.

Overview of fluoroscopically guided robotic instrument placement. (a) Chain of coordinate transforms between the robot, C-arm, patient, and surgical plan, where dotted lines denote identity transform ($I$). The target robot pose ${\widehat{T}}_{\text{base}}^{\text{end}}$ (dashed line) is calculated to align the robot to a target trajectory/position in the preoperative CT image volume. (b) The surgeon uses the aligned instrument as a port to deliver implants through, such as K-wires and screws.

Table 1.

Glossary of symbols used in image-guided robotic instrument placement.

Symbol	Coordinate frame
$T_i^j$	Rigid transform, representing the pose of coordinate frame $i$ with respect to $j$.
wrld	World coordinate frame, equivalent to the $\mathrm{carm}$ coordinate frame below.
carm	Intraoperative fluoroscopic imaging device, e.g., C-arm.
ct	Preoperative CT image of patient.
base	Robot base.
end	Robot end effector, which holds the surgical instrument.
inst	Surgical instrument (e.g., drill guide) manipulated by the robot.
plan	Planned screw trajectory.

2.1.1. Robotically held instrument

End effector pose is described by a set of joint-dependent kinematic equations to determine a transform, $T_{\text{base}}^{\text{end}}$, with respect to the base joint. A surgical instrument is attached to the end effector, and a calibration, $T_{\text{end}}^{\mathrm{inst}}$, relates the instrument coordinate frame to that of the robot. The initial position of the instrument with respect to the robot is thereby $T_{\text{base}}^{\text{end}}{T}_{\text{end}}^{\mathrm{inst}}$.

2.1.2. Image registration

Projections that capture both the patient and robot are used to register the patient to the world coordinate frame (defined as the imaging system coordinate frame) via the patient preoperative CT volume, $T_{\mathrm{wrld}}^{\mathrm{ct}}$, and the robot to the world coordinate frame $T_{\mathrm{wrld}}^{\mathrm{inst}}$ via its attached instrument. The pose of the patient with respect to the robot is thereby ${(T_{\mathrm{wrld}}^{\mathrm{inst}})}^{-1}{T}_{\mathrm{wrld}}^{\mathrm{ct}}$.

2.1.3. Surgical plan

Following registration, the robot places the instrument at a planned trajectory, $T_{\mathrm{ct}}^{\text{plan}}$, preoperatively defined in the patient CT. The new robot pose, ${\widehat{T}}_{\text{base}}^{\text{end}}$, is calculated according to Eq. (1) to servo the robot such that its instrument aligns with the target trajectory, i.e., such that the instrument pose coincides with the plan ($T_{\text{plan}}^{\mathrm{inst}}=I$). To solve for the corresponding robot pose ${\widehat{T}}_{\text{base}}^{\text{end}}$, the plan is related to the end effector of the robot as $T_{\text{plan}}^{\mathrm{inst}}{(T_{\text{end}}^{\mathrm{inst}})}^{-1}$.

2.2. 3D–2D Image Registration

The patient and robot are registered to the world coordinate frame via 3D–2D registration of prior models to intraoperatively acquired radiographs. In the proposed fixed-gantry workflow, the C-arm gantry is kept stationary and radiographs are acquired as the robot manipulates the instrument. The proposed approach is compared to a more conventional rotating-gantry workflow, where the gantry is moved to multiple poses [e.g., anteroposterior (AP) and lateral (LAT)].²⁷

2.2.1. Patient registration

The patient registration is solved by finding an optimal transform that maximizes the similarity between intraoperative radiographs and projections simulated from a preoperative CT. The registration of the patient CT to the world coordinate frame ($T_{\mathrm{wrld}}^{\mathrm{ct}}$) is obtained through optimization of the following objective function:

$$T_{\mathrm{wrld}}^{\mathrm{ct}}=\underset{T}{\arg \max }\sum _{\theta ={\theta }_0}^N\mathrm{GO}[p_{\theta },{\hat{p}}_{\theta }(V_{\mathrm{ct}},T)],$$ (2)

where $N$ is the number of images with projection $p_{\theta }$ acquired at C-arm gantry tilt $\theta$. Digitally reconstructed radiographs (DRRs, ${\widehat{p}}_{\theta }$) are generated by rigidly transforming the preoperative CT, $V_{\mathrm{ct}}$, by $T$ and computing the line integrals corresponding to the C-arm pose for each radiograph. Gradient orientation (GO) similarity metric was chosen owing to its robustness to content mismatch between the CT and projections, such as due to soft tissue deformation imparted during the procedure or the presence of the robot in the radiographs.²⁸ The objective function is optimized using the covariance matrix adaptation evolution strategy (CMA-ES).²⁹

In the scenario referred to as the rotating-gantry workflow, the C-arm is tilted to different poses $\theta$ and registered using Eq. (2). This method takes advantage of multiple perspectives of the pelvis to achieve an accurate registration. In the proposed scenario referred to as the fixed-gantry workflow, the C-arm gantry is kept at a fixed $\theta$, and all acquired projections contain a single view of the patient anatomy with different degrees of occlusion caused by robot motion. It can be challenging to register the anatomy from a single view due to limited triangulation, which increases uncertainties in resolving the position of the object along the direction perpendicular to the imaging plane, referred to here as the depth direction. These challenges, however, are mitigated if the object is sufficiently large, such that it undergoes varying degrees of magnification along the depth direction, and if it is rich in image features (e.g., uniquely oriented gradients). The pelvis is a prime example of such an anatomical object and the fixed-gantry workflow takes advantage of this fact, as demonstrated in prior work to achieve a mean registration accuracy down to 1.3 mm.³⁰

2.2.2. Robot registration

Analogous to the patient registration, the robot is registered by finding an optimal transform that maximizes the similarity between intraoperative radiographs and projections simulated from a CAD model of the robotically held instrument. The registration of the instrument model, ${\kappa }_{\mathrm{inst}}$, to the world coordinate frame ($T_{\mathrm{wrld}}^{\mathrm{inst}}$) is obtained through optimization of the objective function:

$$T_{\mathrm{wrld}}^{\mathrm{inst}}=\underset{T}{\arg \max }\sum _{\theta ={\theta }_0}^N\mathrm{GC}[p_{\theta },{\widehat{p}}_{\theta }({\kappa }_{\mathrm{inst}},T)].$$ (3)

Gradient correlation (GC) similarity metric favors high-intensity gradients that are characteristic of metallic surgical instruments,³¹ unlike GO used in patient registration. The objective function is optimized using the CMA-ES optimizer. Figure 2 shows the combined algorithmic approach for patient and robot registration, which yields the robot pose with respect to the patient.

Fig. 2.

Algorithm for 3D-2D image registration. The pose of the patient with respect to the robot ($T_{\mathrm{inst}}^{\mathrm{ct}}$) is determined by solving for the patient ($T_{\mathrm{wrld}}^{\mathrm{ct}}$) and surgical instrument pose ($T_{\mathrm{wrld}}^{\mathrm{inst}}$) with respect to the imaging system. Prior models of the patient (CT image) and the surgical instrument (CAD model) are initialized at poses ${\tilde{T}}_{\mathrm{wrld}}^{\mathrm{ct}}$ and ${\tilde{T}}_{\mathrm{wrld}}^{\mathrm{inst}}$, respectively. Simulated DRRs are compared to the acquired projections via the GO and GC metric for patient and instrument registration, respectively.

Unlike the extended pelvic anatomy, surgical instruments are small and composed of simple shapes that make it difficult to register from a single view. The fixed-gantry workflow absolves these challenges without tilting the C-arm gantry by instead robotically moving the instrument into multiple poses to acquire projections from different perspectives. Analogous to the rotating-gantry workflow, which uses the relation between C-arm poses to generate DRRs and optimize similarity to the intraoperative projections, the fixed-gantry workflow uses the relation between robot poses to accomplish the same task. Starting with the first robot pose, ${T_0}_{\text{base}}^{\text{end}}$, the corresponding pose of the instrument model in the world coordinate frame is ${\tilde{T}}_{\mathrm{wrld}}^{\mathrm{inst}}$, and the instrument calibration and relation between this first pose and subsequent poses ${T_i}_{\text{base}}^{\text{end}}$ are used to generate DRRs at all robot poses. The first pose, $i=0$, has initial transform ${\tilde{T}}_{\mathrm{wrld}}^{\mathrm{inst}}$, and each subsequent pose has initial transform ${\widetilde{T_i}}_{\mathrm{wrld}}^{\mathrm{inst}}={\tilde{T}}_{\mathrm{wrld}}^{\mathrm{inst}}{(T_{\text{end}}^{\mathrm{inst}})}^{-1}{({T_0}_{\text{base}}^{\text{end}})}^{-1}{T_i}_{\text{base}}^{\text{end}}{T}_{\text{end}}^{\mathrm{inst}}$. Since each robot pose can be related back to the first pose via this equation (assuming negligibly small robot encoder errors), the original CAD model has essentially been replicated and aggregated in the world coordinate frame and this aggregate model is being controlled by the transform of the first pose. Thus, this aggregation increases the apparent complexity and size of the original instrument model in the world coordinate frame, as shown in Fig. 3. A modified objective function can now be optimized,

$$T_{\mathrm{wrld}}^{\mathrm{inst}}=\underset{T}{\arg \max }\sum _{i=1}^M\mathrm{GC}[p_i,{\hat{p}}_i({\kappa }_{\mathrm{inst}},T{(T_{\text{end}}^{\mathrm{inst}})}^{-1}{({T_0}_{\text{base}}^{\text{end}})}^{-1}{T_i}_{\text{base}}^{\text{end}}{T}_{\text{end}}^{\mathrm{inst}})].$$ (4)

where $M$ is the number of acquired projections taken of multiple robot poses, $p_i$ is the projection taken at robot pose $i$, and ${\widehat{p}}_i$ is the DRR corresponding to pose ${T_i}_{\text{base}}^{\text{end}}$.

Fig. 3.

Robot registration in the fixed-gantry workflow. Instead of acquiring multiple radiographs of the surgical instrument at different C-arm poses, the robot is moved to multiple poses (e.g., through rotations of its last joint or other more complex motion profiles) and radiographs are acquired at each robot position. The aggregation of these poses effectively creates a large, complex virtual object that can be registered using Eq. (4).

2.3. Imaging and Robotic Systems

2.3.1. C-arm imaging system

The Cios Spin C-arm (Siemens Healthineers, Erlangen, Germany) is an encoded, calibrated C-arm used in experimental studies. As noted in Sec. 4, the fixed-gantry workflow (as seen in Fig. 3) is also compatible with simple, non-encoded, and non-isocentric C-arms, and the Cios Spin was used in this work as a means to obtain 3D ground-truth definition and allow comparison between the rotating- and fixed-gantry workflows. The system has 3D volumetric imaging capability and an isocentric gantry that is encoded and motorized to a range of $\pm 98\mathrm{deg}$ in the orbital direction and $\pm 220\mathrm{deg}$ in the angular direction, with 116.4-cm source-to-detector distance, 62.3-cm source-to-axis distance, $16\times 16\times 16{\mathrm{cm}}^3$ FOV. Native pixel pitch is 0.152 mm with $1952\times 1952\text{pixels}$ covering a $30\times 30{\mathrm{cm}}^2$ flat-panel detector.³² The system was geometrically calibrated using the two-circle BB phantom method by Cho et al.³³ to solve for the intrinsic parameters (piercing point and source-to-detector distance) and extrinsic parameters (source/detector pose) that define the projective transform for 0.5-deg tilts of the C-arm.

2.3.2. UR5 robot system

The UR5 general purpose robot (Universal Robots, Odense, Denmark) was used for the initial system prototype, noting that the methods described in this paper can be applied to any robotic system that is capable of holding a surgical instrument and actively servoed to new positions. The system is a six degree-of-freedom manipulator with a maximum payload of 5 kg, consisting of a base, shoulder, elbow, and three wrist joints. Its kinematic chain is shown in Fig. 4(a) in terms of Denavit–Hartenberg parameters. The pose of the end effector, which is the attachment point for instruments, is defined by the forward kinematics of all six joints. End effector pose repeatability reported by the manufacturer is 0.1 mm.

Fig. 4.

Robotic system with attached surgical instrument. (a) Kinematic chain of a UR5 robot with an attached drill guide. (b) Drill guide instrument and 3D-printed K-wire adapter. Instrument calibration was performed once offline, by placing the robot at a pose $R_i$ and using known-component registration to localize the instrument, generating a corresponding pose in the C-arm coordinate frame, $C_i$. The calibration, $X$, is the solution to the traditional Hand-Eye calibration problem in Eq. (5).

2.3.3. Surgical instrument and calibration

The instrument used in the studies was a standard surgical drill guide that provides a port through which K-wires/screws can be delivered. A 3D model [Fig. 4(b)] was obtained from a CT of the drill guide. The segmentation threshold value was chosen such that the resulting model best matched various physical measurements of the drill guide (viz. the diameter and shaft length). A K-wire sleeve was 3D-printed from polylactic acid to fit within the drill guide barrel and present an inner diameter with clearance of a standard K-wire (3-mm diameter).

The surgical instrument was rigidly attached to the robot end effector. The calibration of the instrument coordinate frame to the robot end effector coordinate frame follows traditional hand-eye calibration involving measurements of the position of a tool from two fixed reference coordinate frames. The calibration was performed once, offline, and is specific to the instrument used. The robot was servoed to randomly place the instrument at a total of 40 locations within an $8\times 8\times 8{\mathrm{cm}}^3$ volume at the C-arm isocenter. A CBCT scan at each location provided 400 projections of the instrument to perform 3D–2D known-component registration. Thus, at each random position of the instrument, two measurements were obtained: (1) a pose of the robot end effector relative to the base ($T_{\text{base}}^{\text{end}}$); and (2) a pose of the instrument with respect to the C-arm coordinate frame ($T_{\mathrm{wrld}}^{\mathrm{inst}}$).

For any two poses $i$, $j$, the calibration $X$, as shown in Fig. 4(b), is given as

$$\begin{gathered} R_{i}X{C}_i^{-1}=R_{j}X{C}_j^{-1} \\ (R_j^{-1}{R}_i)X=X(C_j^{-1}{C}_i), \end{gathered}$$ (5)

where $R=T_{\text{base}}^{\text{end}}$, $C=T_{\mathrm{wrld}}^{\mathrm{inst}}$, $X=T_{\text{end}}^{\mathrm{inst}}$.

Equation (5) is in the standard $AX=XB$ form for hand-eye calibration, and the calibration $X$ was solved and evaluated across different solvers (detailed in Sec. 2.4.3).

2.3.4. System integration and surgical prototype

The preclinical prototype integrates hardware and software components to interface the imaging system, solve registrations, manipulate the robot, and provide a visual interface to the surgeon. The software architecture adopts the model-view-controller design pattern to separate algorithmic components (model) from hardware interfaces (controller) and the surgical interface (view). Model and controller components were implemented as a series of Jupyter notebooks that are individually responsible for: (1) automatically reading fluoroscopic images and encoder values from the C-arm over a read-only ethernet connection; (2) GPU-accelerated 3D–2D registration of the preoperative patient volume and instrument model; and (3) servoing the robot to planned targets.

The system state is observed by an in-house image guidance platform, called TREK,³⁴ which integrates intraoperative 3D imaging with surgical navigation and is based on the open-source packages cisst (Johns Hopkins University, Baltimore, Maryland) and 3D Slicer (Brigham and Women’s Hospital, Boston, Massachusetts). Acquired images, C-arm gantry, and robot poses sent over OpenIGTLink³⁵ are used to render a virtual scene that allow designation/modification of the target plan and provide a surgical interface to assist the operating surgeon. Figure 5 shows the UR5 module, on the left, which provides the interface to drive the robot to a given pose and an option to visualize the position of the robot in the 3D navigation interface in real-time. The 3D interface includes multi-planar and visualizations of the patient CT, trajectory plans, and real-time tracking of the robot via continuous querying of the robot encoders. A 2D interface is also provided for viewing radiographs augmented with trajectory plans and current positions of the instrument.

Fig. 5.

TREK user interface for robotic instrument positioning, including 2D fluoro augmentation (top right) as well as 3D navigation and visualization of the aligned drill guide (yellow), instrument trajectory and K-wire diameter extent (blue), and preoperative trajectory planning acceptance volumes (green).

The instrument is aligned to the target trajectory by first positioning the robotic arm in a safe working space above the patient in rough proximity to the target trajectory. The robot is then served to align with the axis of the trajectory with a 50-cm offset from the target tip location and then slowly approach the cortical bone entry point with a 5-mm offset. Cooperative control can also be used to allow the surgeon to exert a force to push or pull the robot as the robot is locked on the target trajectory axis.

2.4. Experiments in Phantom and Cadaver

The accuracy of the proposed fixed-gantry workflow was evaluated and compared to the rotating-gantry workflow in a phantom study. Additional data were collected in this study to evaluate mechanical and algorithmic operating parameters for the fixed-gantry workflow. The resulting operating parameters were then validated in a cadaver study that involved drill guide alignment and K-wire placement.

2.4.1. Phantom and cadaver data collection

An anthropomorphic abdomen phantom (The Phantom Laboratory, Greenwich, New York) with a natural human pelvis embedded in tissue-equivalent plastic was used in the phantom study [Fig. 6(a)]. A preoperative CT image of the phantom was acquired from a SOMATOM Definition (Siemens, Erlangen, Germany) scanner, reconstructed on a $0.82\times 0.82\times 0.5{\mathrm{mm}}^3\text{voxel}$ grid with a standard bone-kernel. A total of 8 K-wire trajectories were planned in the CT image, using the TREK interface to designate an entry and end points for each trajectory, as shown in Fig. 6(b). The trajectories were based on eight common fracture sites for pelvic trauma, referencing expert definitions that were defined in previous work.³⁶ Although trajectories were manually defined in these studies, automatic methods also exist³⁶ that can be used to readily provide targets in the OR.

Fig. 6.

Experimental system setup. (a) Setup for phantom experiments, showing the imaging system (Cios Spin), robotic system (UR5), surgical instrument (drill guide), anthropomorphic pelvic phantom, and an overlay of a planned trajectory. (b) Example K-wire trajectory planned in CT using the surgical interface. (c) Setup for cadaver experiments, showing delivery of a K-wire through the robotically held drill guide at target.

For each target trajectory, the phantom and robot were positioned close to the isocenter of the C-arm such that both the anatomical region of interest and the robotically held instrument could be visualized in fluoroscopic images (for 3D–2D guidance) and CBCT (for truth definition and performance evaluation). For registrations using the fixed-gantry workflow, the drill guide was rotated along the last joint of the robot in 10 deg increments along the interval [0 deg, 180 deg] (giving a total of 19 poses) and AP fluoroscopic images were acquired at each rotation. Five projections, evenly spaced over the interval, were used to solve the registrations and drive the robot to the target. For registrations using the rotating-gantry workflow, two projections – AP ($\theta =0\mathrm{deg}$) and oblique ($\theta =30\mathrm{deg}$), were extracted from the set of 400 projections from the first CBCT scan, avoiding highly attenuated views (e.g., LAT, $\theta =90\mathrm{deg}$). Separate CBCT scans of the drill guide were acquired after driving the robot to target. The data were used to analyze the end-to-end drill guide positioning accuracy of the two workflows (Sec. 2.4.4). The data not used for the online registrations (e.g., the additional fluoroscopic images acquired of the robot drill guide) were used to evaluate the operating parameters for the fixed-gantry workflow pertaining to registration (Sec. 2.4.2) and robotic control (Sec. 2.4.3).

A cadaver torso was used to assess the workflow and performance of the fixed-gantry approach in a realistic operating setting, using the parameters determined in the phantom study. Six trajectories were planned in the preoperative CT of the pelvis. For each trajectory, the cadaver was positioned such that the entry point was approximately at isocenter and the robotically held instrument was positioned over the patient within the FOV. Fixed-gantry patient and robot registrations were performed, and the robot was driven to the target trajectory. A CBCT image of the aligned drill guide and patient was acquired. A K-wire was then inserted through the drill guide and soft tissues, bringing the K-wire to an entry point at the cortical surface of the pelvis. A second CBCT scan was acquired with the K-wire inserted at the entry point.

2.4.2. Analysis of 3D–2D image registration

Data that were not used to drive the robot during the experiments was used to determine operating ranges for the fixed-gantry workflow for (1) the tube output setting used for fluoroscopic acquisitions, and (2) the number of robot poses used for registration. These results were compared to conventional rotating-gantry workflow with nominal parameters.

For the evaluation of (1), a nominal x-ray tube output of $0.3\mathrm{mAs}/\text{frame}$ was used. Summation of fluoro images was used to simulate higher x-ray tube output up to $10\times$ the nominal dose, and fixed-gantry (single-view) patient registration was performed at each setting (giving $T_{\mathrm{wrld}}^{\mathrm{ct}}$). Additionally, at each setting, images were denoised using a curvature flow denoising filter³⁷ and registration was compared to ones using images without denoising. To evaluate the registration accuracy, target registration error for patient registration was computed as

$$\mathrm{TRE}=⟨\Vert {\mathbb{T}}_{\mathrm{wrld}}^{\mathrm{ct}}·x_{\mathrm{ct}}-T_{\mathrm{wrld}}^{\mathrm{ct}}·x_{\mathrm{ct}}\Vert ⟩,$$ (6)

where ${\mathbb{T}}_{\mathrm{wrld}}^{\mathrm{ct}}$ is a ground-truth transformation of the preoperative patient CT to the world/C-arm coordinate frame, solved using 3D–2D registration of a large subset ($N=50$) of evenly distributed projections out of the 400 acquired during the pre-registration CBCT scan. $x_{\mathrm{ct}}$ is a set of feature points defined in the pelvis preoperative CT.

For the evaluation of (2), five poses (rotations of the instrument) were used to register and drive the robot. Additional analysis was performed, varying the number of poses from $k=[1\dots 8]$ and performing robot registration using the fixed-gantry workflow (giving $T_{\mathrm{wrld}}^{\mathrm{inst}}$). A total of $n=19$ poses were collected over a range of 0 deg to 180 deg with 10 deg increments for each trajectory. This provides $\left(\begin{array}{c}n\\ k\end{array}\right)$ pose combinations, where the minimum number of $k$-combinations is $\left(\begin{array}{c}n\\ k=1\end{array}\right)=19$. To avoid statistical bias, 19 poses that maximized the angular separation were selected for each value of $k$ – e.g., for $k=2$, first the 10 combinations with 90-deg separation were chosen, followed by nine poses with 80-deg separation. This experiment was repeated using a modified drill guide, as detailed in the Appendix, to evaluate the impact of increasing radiographic features.

The registration accuracy of the robot was considered in terms of its position and orientation, and evaluated as

$$\delta ={({\mathbb{T}}_{\mathrm{wrld}}^{\mathrm{inst}})}^{-1}{T}_{\mathrm{wrld}}^{\mathrm{inst}},$$ (7)

where ${\mathbb{T}}_{\mathrm{wrld}}^{\mathrm{inst}}$ is a ground-truth transformation of the robot at its initial pose before drill guide alignment, and $\delta$ is a $4\times 4$ homogeneous transformation matrix containing a $3\times 3$ rotation matrix R and $3\times 1$ translation vector $x$. The rotation matrix $R$ was defined using Euler angle notation as

$$R=X(\alpha )Y(\beta )Z(\gamma ),$$ (8)

where $X,Y,Z$ represent rotations around their respective axis by angles $\alpha ,\beta ,\gamma$. With $\theta =(\alpha ,\beta ,\gamma )$, translational error was defined as ${\delta }_x=\Vert x\Vert$ and rotational error was defined as ${\delta }_{\theta }=\Vert \theta \Vert$.

2.4.3. Assessment of robot control

Two analyses were performed to assess the sensitivity of drill guide positioning accuracy to (1) the choice of robotic system via an analysis of robot positioning accuracy versus robot encoder repeatability, and (2) the choice of calibration method via an assessment of the $AX=XB$ solver used for instrument calibration.

To analyze the sensitivity to changes in robot encoder repeatability, end effector positioning repeatability error was simulated by randomly perturbing each transform of the pipeline in Eq. (1) that depends on the robot. Included in this list is the robot registration $T_{\mathrm{wrld}}^{\mathrm{inst}}$, which was calculated using the fixed-gantry workflow and invokes relations between robot poses in its algorithm. The magnitude of the perturbations varied from the nominally reported precision of UR5 (0.1 mm) up to 3 mm. Instrument calibration was recomputed using 40 robot poses with random perturbations of the same magnitude, and end-to-end positioning error was measured as in Sec. 2.4.4.

A total of 7 $AX=XB$ solvers were evaluated, including the Park solver used to drive the robot in the phantom study.^38–44 Since the fixed-gantry workflow uses the calibration as part of the algorithm to solve for the robot registration, robot registration was performed using various solvers and was used in Eq. (1) to determine end-to-end robot positioning accuracy as a function of solver. The convergence of accuracy was also evaluated as a function of the number of measurements in Eq. (5).

2.4.4. End-to-end robot positioning accuracy

To evaluate the geometric accuracy of robot drill guide alignment and K-wire placement, ground-truth transformations were calculated by registering the respective CBCTs to the preoperative CT space, yielding ${\mathbb{T}}_{\mathrm{CBCT}}^{\mathrm{CT}}$. Two points, ($x_0$, $x_1$), were then manually designated to delineate the trajectory of the drill guide or K-wire in the CBCT. Tip point error was defined as

$${ϵ}_x=\Vert ({\mathbb{T}}_{\mathrm{CBCT}}^{\mathrm{CT}}{x}_0-x_p)-)){\mathbb{T}}_{\mathrm{CBCT}}^{\mathrm{CT}}{x}_0-x_p)·\stackrel{\hspace{0.17em}\rightharpoonup }{t})\stackrel{\hspace{0.17em}\rightharpoonup }{t}\Vert ,$$ (9)

where $x_p$ is the entry point of the trajectory plan in the preoperative CT and $\stackrel{\hspace{0.17em}\rightharpoonup }{t}$ is the unit vector of vector ${\mathbb{T}}_{\mathrm{CBCT}}^{\mathrm{CT}}(x_1-x_0)$.

The angular deviation ${ϵ}_{\theta }$ between the unit vector trajectory axis ($\stackrel{\hspace{0.17em}\rightharpoonup }{t}$) and unit vector planned trajectory axis ($\stackrel{\hspace{0.17em}\rightharpoonup }{p}$) was evaluated as

$${ϵ}_{\theta }={\cos }^{-1}(\stackrel{\hspace{0.17em}\rightharpoonup }{t}·\stackrel{\hspace{0.17em}\rightharpoonup }{p}).$$ (10)

Deviations of the tip position and angle quantify the alignment error to the target trajectory plan at either the surface of the patient (in the case of drill guide alignment) or at the surface of the pelvis bone (in the case of K-wire placement). However, small errors at this location propagate along the length of the trajectory into the pelvis. Distances to the bone cortex were measured by extrapolating a 3-mm K-wire at the tip point of the aligned drill guide or delivered K-wire and propagating it through a surface mesh representation of the phantom pelvis. The first intersection of this K-wire is the entry point of the trajectory, denoted as position $p=0\mathrm{mm}$. The last intersection is the end point. At discrete points along the length of the trajectory, the closest distance of the K-wire surface model to the pelvis surface mesh is computed, as shown in Fig. 7.

Fig. 7.

Calculation of the proximity of a K-wire to the bone cortex. A sample calculation is illustrated at a position $p=30\mathrm{mm}$ from the entry point of the trajectory. The minimum distance $l_{\min }$ between the virtual K-wire of diameter $d_{\mathrm{k}\text{wire}}$ and the pelvic surface is calculated.

3. Results

3.1. Analysis of 3D–2D Image Registration

3.1.1. Patient registration

As shown in Fig. 8, increasing x-ray tube output from 0.3- to 3-mAs reduced noise and resulted in a modest, but measurable improvement in single-view patient registration accuracy. This is especially evident when using projections with no denoising ($\mathrm{TRE}=1.12\pm 1.67\mathrm{mm}$ at 0.3 mAs versus $\mathrm{TRE}=0.78\pm 0.39\mathrm{mm}$ at 3 mAs). Application of the curvature flow denoising filter resulted in a stable operating range for single-view patient registration accuracy across all evaluated x-ray tube output settings, helped reduce outliers and gave a small increase in accuracy ($\mathrm{TRE}=0.93\pm 0.41\mathrm{mm}$ at 0.3 mAs versus $\mathrm{TRE}=0.75\pm 0.33\mathrm{mm}$ at 3 mAs, $p<0.05$). The results in Fig. 8(a) suggest that following denoising, TRE was relatively stable as a function of dose down to 0.3 mAs, which was chosen as the operating setting to minimize the dose imparted to the patient and the surgical staff.

Fig. 8.

Effect of radiation dose, expressed in terms of x-ray tube output (mAs), in fixed-gantry workflow. (a) TRE as a function of dose level used for patient registration with a single projection, with exponential fits to means, when using projections without denoising versus denoised projections. (b) Projection ROI at various dose settings. Noise ($\sigma$) was calculated in a 4 × 4 ROI (in magenta) and reported in arbitrary detector units (ADU).

Since the fixed-gantry workflow provides multiple projections of the patient as the robot is moved to different poses, all $M$ projections that are acquired for robot registration in Eq. (4) can be used to solve the patient registration in Eq. (2) at a fixed $\theta$ (and where $M=N$), analogous to summation of $M$ fluoroscopic frames. Thus, a nominal setting of 0.3 mAs and a fixed-gantry workflow using five projections is analogous to registration with one projection acquired at 1.5 mAs and gives a marginal improvement in registration accuracy. Registrations using disparate views provided by the rotating-gantry workflow performed significantly better than registration from a single view with ($\mathrm{TRE}=0.32\pm 0.22\mathrm{mm}$ at 0.6-mAs total for two projections, $p<0.05$); however, both workflows performed with $\mathrm{TRE}<1\mathrm{mm}$.

3.1.2. Robot registration

The results in Fig. 9 show the improvement in registration accuracy with respect to increasing number of robot poses used in the registration, with an overall ${\delta }_x$ of $1.96\pm 2.81\mathrm{mm}$ for one pose and $0.81\pm 0.31\mathrm{mm}$ for eight poses. The rotating-gantry workflow achieved significantly better registration accuracy with two C-arm poses (${\delta }_x=0.52\pm 0.30\mathrm{mm}$) compared to the fixed-gantry workflow with eight poses ($p<0.01$); however, with as few as three robot poses, the fixed-gantry workflow still achieved accurate registration with ${\delta }_x$ $<1\mathrm{mm}$. The ability to exercise greater rotational disparity in between projections when using the fixed-gantry workflow resulted in improved rotational geometric accuracy compared to the rotating-gantry workflow (${\delta }_{\theta }=0.14\pm 0.06\mathrm{deg}$ with eight robot poses versus ${\delta }_{\theta }=0.48\pm 0.76\mathrm{deg}$ with 2 C-arm poses, $p<0.01$). The results were similar for the modified drill guide, detailed in the Appendix, with marginal improvements in registration accuracy due to the larger size and additional image features.

Fig. 9.

Effect of rotating the robot (fixed-gantry workflow) versus rotating the C-arm (rotating-gantry workflow) for robot registration. (a) ${\delta }_x$ as a function of number of robot poses used for robot registration in the robot motion workflow, compared to (b) ${\delta }_x$ for two C-arm poses in the rotating-gantry workflow. Exponential functions were fit to the median of ${\delta }_x$ in (a). (c) Angular error (${\delta }_{\theta }$) as a function of number of robot poses used for robot registration in the robot motion workflow, compared to (d) ${\delta }_{\theta }$ for two C-arm poses in the rotating-gantry workflow, with an exponential fit to the median.

There is a tradeoff between geometric registration accuracy, dose, and workflow when selecting the number of poses to perform fixed-gantry registration: as the number of poses increases, registration accuracy improves, but dose and projection acquisition time also increase. Based on the results in Figs. 9(a) and 9(c), nominal value of five robot poses was chosen to mitigate these tradeoffs, with ${\delta }_x=0.81\pm 0.35\mathrm{mm}$ and ${\delta }_{\theta }=0.15\pm 0.06\mathrm{deg}$.

3.2. Assessment of Robot Control

3.2.1. Robot end effector positioning repeatability

All robotic systems have an inherent precision in repeated positioning of its end effector, which is reported to be 0.1 mm for the UR5. The results shown in Fig. 10 reflect the end-to-end robot positioning accuracy that results from such random amounts of precision error injected into the pipeline of Eq. (1), including injecting error into the poses and calibration used for registration of the robot in the fixed-gantry workflow. The results indicate that for the fixed-gantry workflow, the combination of end effector positioning repeatability and mechanical stress-induced positioning error should not exceed 1.7 mm to achieve median ${ϵ}_x<2\mathrm{mm}$, or 3.2 mm to achieve median ${ϵ}_{\theta }<1\mathrm{deg}$. The end effector repeatability of the UR5 robotic system was found to exhibit very low variation in robot tip-point and angular deviation (0.2 mm and 0.06 deg, respectively).

Fig. 10.

End-to-end robotic positioning accuracy as a function of end effector positioning repeatability. (a) ${ϵ}_x$ as a function of end effector positioning repeatability. The limits of the gray area represent the 25th and 75th percentile of the data, and the dashed line represents the median. UR5 end effector positioning repeatability is labeled as $x_{\mathrm{UR}5}$. To achieve median ${ϵ}_x$ of 2 mm, the maximum allowable encoder repeatability is 1.5 mm. (b) ${ϵ}_{\theta }$ as a function of encoder repeatability. To achieve median ${ϵ}_{\theta }$ of 1 deg, the maximum allowable encoder repeatability is 3.2 mm.

3.2.2. Instrument calibration

Figure 11(a) shows that all solvers perform similarly in end-to-end tip-point deviation. The solver by Park and Martin³⁸ was nominally chosen for phantom experimentation based on preliminary studies perform by Yi et al.²⁶ that examined the precision/repeatability of solvers [in contrast, the work presented here examines the accuracy using the full robot pipeline of Eq. (1)]. The solver by Tsai and Lenz⁴⁴ was observed to be more sensitive to measurement noise. Figure 11(b) shows the relationship between the end-to-end tip point deviation and the number of measurements used to solve the calibration using the Park solver. A clear improvement in tip-point deviation is evident up to roughly 12 measurements, with little to no improvement for greater numbers of measurements. These results suggest that the nominal choice of 40 measurements used in the phantom experiments was an appropriate amount of measurements to ensure accurate instrument calibration.

Fig. 11.

End-to-end positioning accuracy as a function of solver and number of measurements. (a) Comparison of $AX=XB$ solvers for instrument calibration. (b) Simulated end-to-end accuracy for Park solver as a function of number of measurements used to perform the instrument calibration, with an exponential fit to the means overlaid in red.

3.3. End-to-End Accuracy of Fixed-Gantry versus Rotating-Gantry

The phantom study demonstrated the feasibility of the proposed fixed-gantry workflow with an average tip-point deviation ${ϵ}_x=1.57\pm 0.47\mathrm{mm}$ and an average angular deviation ${ϵ}_{\theta }=0.35\pm 0.32\mathrm{deg}$, as shown in Fig. 12. The rotating-gantry workflow outperformed the fixed-gantry workflow in terms of tip-point deviation (${ϵ}_x=0.83\pm 0.47\mathrm{mm}$ versus ${ϵ}_x=1.57\pm 0.47\mathrm{mm}$, respectively; $p<0.05$). The fixed-gantry workflow performed similarly to the rotating-gantry workflow in angular deviation (mean ${ϵ}_{\theta }=0.35\pm 0.32\mathrm{deg}$ versus ${ϵ}_{\theta }=0.29\pm 0.15\mathrm{deg}$, respectively).

Fig. 12.

Robot positioning accuracy in phantom. (a) Robot tip positioning error ${ϵ}_x$ for fixed-gantry workflow (five robot poses) and rotating-gantry workflow (two C-arm poses). (b) Angular error ${ϵ}_{\theta }$ for fixed-gantry workflow (five robot poses) and rotating-gantry workflow (two C-arm poses).

Figure 13 plots the distance from the K-wire to cortical bone along the length of the trajectory, as described in Sec. 2.4.2 and Fig. 7, showing the conformance of K-wire within bone corridors. Negative distances indicate breach of the cortex. For reference, the plots also show the bone distance profile of a K-wire perfectly aligned with the trajectory plan (black). For all trajectories executed with both the rotating- and fixed-gantry workflow (magenta and green respectively), the simulated K-wires reside within bone corridors with safe margins. This suggests that despite significant differences in tip-point deviation between the two workflows, both performed similarly and safely when the error was propagated forward along the trajectory. The figure also shows the results of the study that substituted all combinations of five poses from the full dataset described in section Sec. 2.4 and determined the proximity of simulated 3-mm diameter K-wires to the pelvic cortex for all combinations. The light-green region shows the range across all combinations. It is evident that for seven out of the eight trajectories in the study, the particular choice of poses did not affect the conformance of simulated K-wires in cortical bone, with only one trajectory (right sacroiliac) experiencing a mild ($<0.5\mathrm{mm}$) breach for a subset of combinations.

Fig. 13.

Distance of extrapolated K-wires from the bone cortex, in phantom. $\text{Distances}<0\mathrm{mm}$ indicate breach of the cortical wall by a 3-mm diameter K-wire. The black line indicates a best-case reference in which the K-wire is aligned perfectly to the preoperative trajectory plan. The green and magenta lines indicate the breach distance for the fixed- and rotating-gantry workflows, respectively, in the phantom study, the light-green region represents the range of breach distances that occur when substituting various five-pose combinations for fixed-gantry registration.

3.4. Fixed-Gantry Robot Positioning Accuracy in Cadaver

The end-to-end accuracy of robot positioning was evaluated at: (1) initial alignment of the drill guide to a trajectory plan; and (2) placement of the K-wire at the cortical surface of the pelvis. Figure 14 shows the entry-point error ${ϵ}_x$ and axis alignment error ${ϵ}_{\theta }$ at each time point for all trajectories. Tip-point alignment error of $1.42\pm 0.71\mathrm{mm}$ and axis alignment error of $0.52\pm 0.25\mathrm{deg}$ was observed. Despite accurate alignment of the drill guide to within 2 mm and 1 deg of the trajectory plan (similar to the results observed in phantom), there were noticeable increases in error as the K-wire was delivered through the cortical surface of the cadaver pelvis. The reason for increased error is deflection (“skiving”) of the K-wire against the highly angulated bone entrance surface. Further contributing to the skiving effect was the simple drill guide adapter sleeve (plastic insert) that did not adequately constrain the K-wire from deflecting. It is also possible that the end effector of the UR5 is not sufficiently stiff to be able to withstand shearing forces.

Fig. 14.

Accuracy of drill guide alignment and placement of K-wire at the cortical surface of the pelvis. (a) Tip-point alignment error. (b) Axis alignment error. (c) 3D visualization in CT of aligned drill guide with manually delineated K-wire trajectory and trajectory plan.

Figure 15 shows that for all 6 trajectories, K-wire trajectories extrapolated from the aligned drill guide did not breach the pelvis, confirming the performance of the fixed-gantry registration in aligning the drill guide to a target trajectory. As the K-wire was extended to the cortical surface of the bone (through the incision of muscle and fat), deflections were noted on a case-by-case basis.

Fig. 15.

Distance of extrapolated K-wires from the pelvic cortex, in cadaver. $\text{Distances}<0\mathrm{mm}$ indicate breach of the cortical wall by a simulated 3-mm diameter K-wire.

As shown in Fig. 15, trajectories to the anterior inferior iliac spine (AIIS 1, AIIS 2) and the iliac crest showed close agreement between the plan and both checkpoints (superficial and cortical surface). The posterior superior ramus and sacroiliac trajectories performed similarly, with marginally higher deviations occurring during placement of the K-wire at the bone surface due to minor deflections; however not large enough to cause a breach. The anterior superior ramus trajectory was a challenging case in which the K-wire deflected at the steep angular bone surface when placing the K-wire at the entry point. This deviation resulted in $\sim 1\text{-}\mathrm{mm}$ breach spanning $\sim 3\mathrm{mm}$ and significant deviation from the trajectory plan (${ϵ}_x\sim 7\mathrm{mm}$, ${ϵ}_{\theta }\sim 3\mathrm{deg}$). These results demonstrate that despite mechanical stresses and skiving in gaining bone purchase and drilling, the robot registration and guidance were accurate, and K-wire paths generally conformed within bone corridors without breach. More robust mechanical engineering of the drill guide sleeve would presumably reduce the skiving effect—an important consideration for eventual translation to clinical use.

4. Discussion and Conclusions

A novel solution was presented for fluoroscopic guidance of robotic instrument placement and demonstrated in the context of pelvic trauma surgery. The method uses fluoroscopic projections of the operating scene (routinely acquired with a mobile C-arm) and uses precise encoded motion of the robot to obtain multiple views of the attached surgical instrument, thus avoiding the need for C-arm gantry motion to achieve accurate 3D–2D registration. When evaluating the end-to-end drill guide alignment error of the fixed-gantry workflow compared to the rotating-gantry workflow, both achieved alignment accuracy within 2 mm and 1 deg of the planned trajectory, comparable in accuracy to tracker-based solutions.^10,26 The extrapolated path of the K-wire from the aligned drill guide remained safely within bone corridors for all executed trajectories.

Fixed-gantry registration of the robot achieved comparable registration accuracy to rotating-gantry registration with errors $<1\mathrm{mm}$ and 0.2 deg when using five rotations of the drill guide. The fixed-gantry workflow can exercise large rotational disparity between views of the instrument compared to the rotating-gantry workflow. This improved rotational disparity does not help mitigate the depth resolution challenges that create a tip-point deviation difference between the two workflows; however, it likely the reason that there is an improvement in the rotational resolution of the instrument during robot registration, which may explain why the fixed-gantry workflow performs better than the rotating-gantry workflow in angular deviation. It is likely that in addition to the number of robot poses, certain positions and orientations of the robot in the imaging FOV may provide views of the instrument with greater information content. However, simply obtaining more poses of the robot increases the likelihood of capturing favorable views of the instrument, which may explain the improvement in average registration accuracy demonstrated in this work.

An analysis of the patient registration indicates that both the fixed-gantry and rotating-gantry workflows performed with registration accuracy better than 1 mm at a dose of 0.3 mAs, supporting the notion that the pelvis is a gradient-rich, extended object amenable to single-view registration (as in the fixed-gantry workflow) that is comparable in accuracy to multi-view registration (as in the rotating-gantry workflow) at a low dose setting.

While both workflows performed similarly, the fixed-gantry workflow has several advantages. It solves the registration without a need to move the C-arm as in the rotating-gantry workflow, instead relying on encoded robot motion for robot registration and relying on the size and shape of the pelvis to achieve patient registration. This simplifies and expedites the registration of image-guided robotic assistants because (1) collisions with a moving gantry no longer need to be considered and (2) there is greater flexibility in placing the patient and robot within the imaging field of view since they do not need to be visible in more than one fluoroscopic perspective. Extending the size and features of the instrument in 3D may improve registration accuracy, as demonstrated in the Appendix, but may also hinder the surgeon’s use of the instrument or be too large to capture within the FOV. The fixed-gantry workflow avoids these challenges by capturing radiographs at different robot poses to build up a set of extended features to improve the robustness of registration.

While an encoded, calibrated C-arm (Cios Spin) was used in this work for purposes of ground-truth definition, the fixed-gantry workflow is compatible with simple, non-calibrated, non-encoded, and non-isocentric C-arm systems in mainstream use since there is no need to geometrically relate projections acquired at multiple perspectives for DRR generation and registration. This calibration-free method, previously reported by Ref. 45, essentially uses the patient anatomy as the reference object to iteratively solve for the extrinsic and intrinsic parameters of the C-arm system geometry (nine degrees of freedom). Use of this method within our solution therefore provides a C-arm calibration, which is in turn used for robot registration.

The system also offers to reduce radiation dose to the patient and surgical staff. For example, a typical single-screw placement for anterior pelvic ring fractures is reported to have mean fluoroscopy time of 19 s,⁴⁶ compared to as little as 0.5 s to acquire five projections at $10\text{frames}/\mathrm{s}$ of the patient and robot in the fixed-gantry workflow.

The cadaver study translated the fixed-gantry workflow and operating parameters to realistic conditions and achieved entry point drill guide alignment error of $1.42\pm 0.71\mathrm{mm}$ and axis alignment error of $0.52\pm 0.25\mathrm{deg}$. Increases in error were observed as a K-wire was placed through the aligned drill guide, primarily due to mechanical stresses and skiving in gaining bone purchase and drilling. Future preclinical evaluation will focus on improving the mechanical stability of the robotic system to better preserve the accuracy of the drill guide against skiving at the bone surface. Clinical systems appear to resist such skiving—for example, the ExcelsiusGPS robot, specified to withstand 180 lbs of force at its end effector. Future studies prior to clinical translation are planned, involving a cohort of residents and orthopaedic surgeons to better establish the safety of the system, obtain user feedback on interaction with the surgical interface, and measure workflow parameters (e.g., radiation dose and procedure time).

In orthopaedic pelvic trauma surgery, measures are taken to ensure that the patient is secure to avoid motion of bone fragments during reduction or implant placement; however, motion is still possible. In the event of patient motion, only the patient registration requires an update, which can be achieved with as little as one image using the single-view approach. Such a registration takes $\sim 60$ iterations with an average runtime of 0.5 s/iteration using our research prototype. Future work will investigate the feasibility of mounting a camera on the robot to detect and/or track patient movement and alert the surgeon to acquire new projections as necessary.

The current prototype robot must first be positioned in the vicinity of the target trajectory to avoid collisions of the arm as it moves linearly from this position and locks onto the target trajectory axis. A future iteration of the system may instead be constructed as a cooperative robot (COBOT) that uses virtual fixtures⁴⁷ to guide the surgeon in physically moving and aligning the robot onto a target trajectory with tactile feedback. This would give the surgeon a hands-on approach to safely manipulate the robot and avoid collisions with the patient, imaging device, and OR equipment.

The presented method shows promise as a way to streamline not just for pelvic K-wire placement but may also find utility in other high-fluoro orthopaedic procedures, such as pelvis fracture reduction robots that hold or manipulates bone fragments through via orthopaedic pins.⁴⁸ The methods described here can be applied to any robotic task for a different procedure, with the only requirements being that a CAD model of the robotically held instrument (either through the manufacturer or from a laser-range scan or CT of the tool), and appropriate planning to provide a target destination in the patient CT for the robot to drive toward (for instance, automatic planning of femoral stem implants in total hip arthroplasty⁴⁹). In this way, the method may facilitate broader application and adoption of robotic-assistance systems in orthopaedic trauma surgery.

5. Appendix: Impact of Instrument Design on Registration Accuracy

A phantom study was performed to evaluate the impact of increasing size and distribution of radiographic features on registration accuracy. A steel rod was attached orthogonal to the drill guide to create the extended T-shaped structure shown in Figs. 16(a) and 16(b). A CAD model was generated for the extended design [Fig. 16(c)], and the study detailed in Sec. 2.4.1 was repeated to assess the hypothesized improvement in registration accuracy.

Fig. 16.

Registration accuracy with a modified drill guide. (a) and (b) The modified design features a steel rod perpendicular to the drill guide. (c) CAD model of the original (red) and modified attachment (blue). (d) Fluoroscopic image of the modified drill guide. (e) Registration accuracy versus the number of robot poses (as in Fig. 9), showing that the modified drill guide reduced mean error for 1–2 poses.

As shown in Fig. 16(e), the modified drill guide improved registration accuracy for $n=1$ robot pose, achieving similar mean performance with 1 robot pose (${\delta }_x=0.89\pm 1.50\mathrm{mm}$) as with 2 robot poses of the original drill guide (${\delta }_x=0.94\pm 1.81\mathrm{mm}$). The additional image features introduced by the orthogonal rod is analogous to multi-pose registration of the original guide with a 90 deg rotation between poses. As such, there was no statistically significant difference in registration accuracy for $n>2$ poses.

Biography

Biographies of the authors are not available.

Disclosures

No conflicts of interest, financial or otherwise, are declared by the authors. This research was supported by academic-industry partnership with Siemens Healthineers (Erlangen Germany).