Computation and validation of intra-operative camera uncertainty

We present a simple method for computing uncertainty in an optical tracking system. Our significant contribution is that the covariance estimates produced by our tracking algorithm are shown to closely match lower bounds established by Ohta and Kanatani [13]. Our work addresses the existence of uncertainty in tracking and is a step toward a complete estimate of intra-operative uncertainty in computer-assisted surgery.

Patellofemoral joint kinematics in individuals with and without patellofemoral pain syndrome

BACKGROUND

Patellofemoral pain syndrome is a prevalent condition in young people. While it is widely believed that abnormal patellar tracking plays a role in the development of patellofemoral pain syndrome, this link has not been established. The purpose of this cross-sectional case-control study was to test the hypothesis that patterns of patellar spin, tilt, and lateral translation make it possible to distinguish individuals with patellofemoral pain syndrome and clinical evidence of patellar malalignment from those with patellofemoral pain syndrome and no clinical evidence of malalignment and from individuals with no knee problems.

METHODS

Three-dimensional patellofemoral joint kinematics in one knee of each of sixty volunteers (twenty in each group described above) were assessed with use of a new, validated magnetic resonance imaging-based method. Static low-resolution scans of the loaded knee were acquired at five different angles of knee flexion (ranging between -4 degrees and 60 degrees). High-resolution geometric models of the patella, femur, and tibia and associated coordinate axes were registered to the bone positions on the low-resolution scans to determine the patellar motion as a function of knee flexion angle. Hierarchical modeling was used to identify group differences in patterns of patellar spin, tilt, and lateral translation.

RESULTS

No differences in the overall pattern of patellar motion were observed among groups (p>0.08 for all global maximum likelihood ratio tests). Features of patellar spin and tilt patterns varied greatly between subjects across all three groups, and no significant group differences were detected. At 19 degrees of knee flexion, the patellae in the group with patellofemoral pain and clinical evidence of malalignment were positioned an average of 2.25 mm more laterally than the patellae in the control group, and this difference was marginally significant (p=0.049). Other features of the pattern of lateral translation did not differ, and large overlaps in values were observed across all groups.

CONCLUSIONS

It cannot be determined from our cross-sectional study whether the more lateral position of the patella in the group with clinical evidence of malalignment preceded or followed the onset of symptoms. It is clear from the data that an individual with patellofemoral pain syndrome cannot be distinguished from a control subject by examining patterns of spin, tilt, or lateral translation of the patella, even when clinical evidence of mechanical abnormality was observed.

A system for ultrasound-guided computer-assisted orthopaedic surgery

Current computer-assisted orthopedic surgery (CAOS) systems typically use preoperative computed tomography (CT) and intraoperative fluoroscopy as their imaging modalities. Because these imaging tools use X-rays, both patients and surgeons are exposed to ionizing radiation that may cause long-term health damage. To register the patient with the preoperative surgical plan, these techniques require tracking of the targeted anatomy by invasively mounting a tracking device on the patient, which results in extra pain and may prolong recovery time. The mounting procedure also leads to a major difficulty of using these approaches to track small bones or mobile fractures. Furthermore, it is practically impossible to mount a heavy tracking device on a small bone, which thus restricts the use of CAOS techniques. This article presents a novel CAOS method that employs 2D ultrasound (US) as the imaging modality. Medical US is non-ionizing and real-time, and our proposed method does not require any invasive mounting procedures. Experiments have shown that the proposed registration technique has sub-millimetric accuracy in localizing the best match between the intraoperative and preoperative images, demonstrating great potential for orthopedic applications. This method has some significant advantages over previously reported US-guided CAOS techniques: it requires no segmentation and employs only a few US images to accurately and robustly localize the patient. Preliminary laboratory results on both a radius-bone phantom and human subjects are presented.

Three-dimensional analysis of alignment error in using femoral intramedullary guides in unicompartmental knee arthroplasty

We used computerized simulations with 3-dimensional models of 20 cadaver femora, calculated from computed tomographic scans, and a model of a rod measuring 200 x 5 mm to study femoral alignment accuracy for unicompartmental knee arthroplasty via minimally invasive reconstruction. The anatomical axis and insertion site were identified on each femur. A simulation of all feasible flexion-extension and varus-valgus orientations was performed. The average rod orientation was 3.2 degrees flexion and 2.5 degrees valgus. The range of orientation was 3.2 degrees extension to 9.7 degrees flexion and 4.5 degrees varus to 8.9 degrees valgus. The study suggests that a short narrow intramedullary rod inserted according to the manufacturer's specifications does not accurately find the anatomical axis and may lead to poor alignment of the femoral prosthesis. Given our finding of consistent bias toward excessive flexion and valgus alignment, we recommend that the operating surgeon carefully plan the insertion point of the intramedullary rod during surgery to compensate for this bias.

An inverse kinematics model for post-operative knee. Ligament parameters estimation from knee motion

A motion-based Inverse Kinematics Knee (IKK) model was developed for Total Knee Replacement (TKR) joints. By tracking a sequence of passive knee motion, the IKK model estimated ligament properties such as insertion locations. The formulation of the IKK model embedded a Forward Kinematics Knee (FKK) model in a numerical optimization algorithm known as the Unscented Kalman Filter. Simulation results performed on a semi-constrained TKR design suggested that ligament insertions could be accurately estimated in the medial-lateral (ML) and the proximal-distal (PD) directions, but less reliably in the anterior-posterior (AP) direction for the tibial component. However, the forward kinematics produced by both the true and estimated ligament properties were nearly identical, suggesting that the IKK model recovered a kinematically equivalent set of ligament properties. These results imply that it may not be necessary to use a patient-specific CT or MRI scan to locate ligaments, which considerably widens potential applications of kinematic-based total knee replacement.

Fast assessment of acetabular coverage using stereoscopic volume rendering

Previous CT-based methods of measuring acetabular coverage of the femoral head have either been labor-intensive or have required extensive preprocessing of the data prior to visualization. We propose a method of measuring acetabular coverage using stereoscopic digitally reconstructed radiographs that required very little labor or image preprocessing time. Taking a craniocaudal view of the pelvis, we measured both preoperative and postoperative CTs of 10 patients treated with transtrochanteric periacetabular osteotomy. Measurements were then made in both monocular and stereoscopic rendering modes. Our method is fast, easy, and provides an intuitive means of visualizing an orthopedic parameter that is important in the progression of early hip arthritis.

Analytic Expressions for Fiducial and Surface Target Registration Error

We propose and test analytic equations for approximating expected fiducial and surface target registration error (TRE). The equations are derived from a spatial stiffness model of registration. The fiducial TRE equation is equivalent to one presented by. We believe that the surface TRE equation is novel, and we provide evidence from computer simulations to support the accuracy of the approximation.

Needle artifact localization in 3T MR images

This work explores an image-based approach for localizing needles during MRI-guided interventions, for the purpose of tracking and navigation. Susceptibility artifacts for several needles of varying thickness were imaged, in phantoms, using a 3 tesla MRI system, under a variety of conditions. The relationship between the true needle positions and the locations of artifacts within the images, determined both by manual and automatic segmentation methods, have been quantified and are presented here.

Computer-assisted guidewire insertion for hip fracture fixation

OBJECTIVE

: This study was designed to test in a laboratory setting a novel computer-assisted fluoroscopic technique and a conventional fluoroscopic technique for open reduction and internal fixation (ORIF) of hip fractures. Our hypothesis is that a novel computer-assisted fluoroscopic technique will achieve acceptable guidewire placement in one pass, with decreased fluoroscopic time and with accuracy and precision better than conventional technique.

DESIGN

Prospective, randomized trials.

SETTING

Laboratory.

PARTICIPANTS

Thirty, Sawbone, femur phantoms.

INTERVENTION

Dynamic hip screw guidewires were inserted into 15 femur phantoms under fluoroscopic guidance by using computer-assisted fluoroscopic ORIF technique, and 15 femurs were inserted by using a conventional fluoroscopic-assisted ORIF technique.

MAIN OUTCOME MEASUREMENTS

Ideal guidewire placement was defined as the center of the femoral head, 5 mm from the apical bone edge on anteroposterior and lateral views. Accuracy was measured as distance to ideal placement, and the number of passes and fluoroscopic time were noted for each trial.

RESULTS

The computer-assisted technique achieved an average guidewire placement that was as accurate as the conventional technique in fewer passes, 1.1 +/- 0.2 (mean +/- standard deviation) compared with 2.4 +/- 1.1 (P < 0.0001), respectively, and with fewer fluoroscopic images, 2 +/- 0 compared with 13.5 +/- 3 (P < 0.0002), respectively. Guidewire placement in both groups was within the tip-apex distance defined by Baumgaertner et al.

CONCLUSIONS

The computer-assisted technique was significantly more accurate and precise than conventional technique. It also required fewer drill tracks through the femur and exposed the patient and the surgical team to significantly less ionizing radiation.

An estimation/correction algorithm for detecting bone edges in CT images

The normal direction of the bone contour in computed tomography (CT) images provides important anatomical information and can guide segmentation algorithms. Since various bones in CT images have different sizes, and the intensity values of bone pixels are generally nonuniform and noisy, estimation of the normal direction using a single scale is not reliable. We propose a multiscale approach to estimate the normal direction of bone edges. The reliability of the estimation is calculated from the estimated results and, after re-scaling, the reliability is used to further correct the normal direction. The optimal scale at each point is obtained while estimating the normal direction; this scale is then used in a simple edge detector. Our experimental results have shown that use of this estimated/corrected normal direction improves the segmentation quality by decreasing the number of unexpected edges and discontinuities (gaps) of real contours. The corrected normal direction could also be used in postprocessing to delete false edges. Our segmentation algorithm is automatic, and its performance is evaluated on CT images of the human pelvis, leg, and wrist.

Magnetic resonance imaging for in vivo assessment of three-dimensional patellar tracking

We have developed a non-invasive measurement technique which can ultimately be used to quantify three-dimensional patellar kinematics of human subjects for a range of static positions of loaded flexion and assessed its accuracy. Knee models obtained by segmenting and reconstructing one high-resolution scan of the knee were registered to bone outlines obtained by segmenting fast, low-resolution scans of the knee in static loaded flexion. We compared patellar tracking measurements made using the new method to measurements made using Roentgen stereophotogrammetric analysis in three cadaver knee specimens loaded through a range of flexion in a test rig. The error in patellar spin and tilt measurements was less than 1.02 degrees and the error in lateral patellar shift was 0.88 mm. Sagittal plane scans provided more accurate final measurements of patellar spin and tilt, whereas axial plane scans provided more accurate measurements of lateral translation and patellar flexion. Halving the number of slices did not increase measurement error significantly, which suggests that scan times can be reduced without reducing accuracy significantly. The method is particularly useful for multiple measurements on the same subject because the high-resolution bone-models need only be created once; thus, the potential variability in coordinate axes assignment and model segmentation during subsequent measurements is removed.

A point-selection algorithm based on spatial-stiffness analysis of rigid registration

OBJECTIVE

We propose a model of shape-based registration that leads to a task-specific algorithm for preoperatively selecting a set of model registration points.

MATERIALS AND METHODS

We performed five sets of computer simulations using registration points generated by our algorithm and two noise amplification index (NAI) algorithms on the basis of the research of Simon 20. We used several different bone surface models (distal radius, proximal femur and tibia) computed from CT images of patient volunteers. The number of registration points used varied between 6 and 30.

RESULTS

Our algorithm was faster than the NAI-based algorithms by factors of approximately 4 and 200. It had equal or better performance in terms of target registration error (TRE) when compared with the other algorithms. Our simulations also showed that point selection can have a large effect on TRE behavior; in particular, poor point selection does not necessarily decrease TRE as more registration points are added.

CONCLUSIONS

Our point-selection algorithm produces model registration points with similar or better TRE behavior than the NAI-based algorithms we tested, and it does so with significantly less computation time.

2D/3D Deformable Registration Using a Hybrid Atlas

Statistical atlases built by point distribution models (PDMs) using a novel hybrid 3D shape model were used for surface reconstruction. The hybrid shape model removes the need for global scaling in aligning training examples and instance generation, thereby allowing the PDM to capture a wider range of variations. The atlases can be used to reconstruct, or deformably register, the surface model of an object from just two to four 2D x-ray projections of the object. The methods was tested using proximal and distal femurs. Results of simulated projections and fluoroscopic images of cadaver knees show that the new instances can be registered with an accuracy of about 2 mm.

Kinematic geometry of osteotomies

This paper presents a novel method for defining an osteotomy that can be used to represent all types of osteotomy procedures. In essence, we model an osteotomy as a lower-pair mechanical joint to derive the kinematic geometry of the osteotomy. This method was implemented using a commercially available animation software suite in order to simulate a variety of osteotomy procedures. Two osteotomy procedures are presented for a femoral malunion in order to demonstrate the advantages of our kinematic model in developing optimal osteotomy plans. The benefits of this kinematic model include the ability to evaluate the effects of various kinds of osteotomy and the elimination of potentially error-prone radiographic assessment of deformities.

Unified Point Selection and Surface-Based Registration Using a Particle Filter

We propose an algorithm for jointly performing registration point selection and interactive, rigid, surface-based registration. The registration is computed using a particle filter that outputs a sampled representation of the distribution of the registration parameters. The distribution is propagated through a point selection algorithm derived from a stiffness model of surface-based registration, allowing the selection algorithm to incorporate knowledge of the uncertainties in the registration parameters. We show that the behavior of target registration error improves as the quality measure of the registration points increases.

Computer-assisted deformity correction using the ilizarov method

The Taylor spatial frame is a fixation device used to implement the Ilizarov method of bone deformity correction to gradually distract an osteotomized bone at regular intervals, according to a prescribed schedule. We improve the accuracy of Ilizarov's method of osteogenesis by preoperatively planning the correction, intraoperatively measuring the location of the frame relative to the patient, and computing the final shape of the frame. In four of five tibial phantom experiments, we were able to achieve correction errors of less than 2 degrees of total rotation. We also demonstrate how registration uncertainty can be propagated through the planned transformation to visualize the range of possible correction outcomes. Our method is an improvement over an existing computer-assisted technique (Iyun et al.) in that the surgeon has the same flexibility as in the conventional technique when fixating the frame to the patient.

Ligament Strains Predict Knee Motion After Total Joint Replacement

A passive forward kinematics knee model was used to predict knee motion of a total joint replacement. Given ajoint angle, maps of articular surfaces, and patient-specific ligament properties, this model predicted femorotibial contact locations based on the principle of ligament-strain minimization. The model was validated by physical experiments on a commonly implanted knee prosthesis, showing excellent correspondence between the model and actual physical motion. Results suggest that the knee prosthesis studied required an intact posterior cruciate ligament to induce the desirable roll-back motion, and that a single-bundle model of major knee ligaments generated kinematics similar to that of a multibundle ligament model. Implications are that a passive model may predict knee kinematics of a given patient, so it may be possible to optimize the implantation of a prosthesis intraoperatively.

Experimental Validation of a 3D Dynamic Finite-Element Model of a Total Knee Replacement

A 3D forward-dynamics model of a total knee replacement was developed using an explicit finite-element package. The model incorporated both a tibiofemoral and a patellofemoral joint and allowed full 6-DOF kinematics for both joints. Simulated quadriceps contraction was used to drive the model. For validation, a unique experimental apparatus was constructed to simulate an open-chain extension motion under quadriceps control. The ligamentous constraints of the MCL and LCL were simulated using tension springs. The kinematics of the tibia and patella were recorded along with the net forces and moments applied to the femur. Several ligament and inertial configurations were simulated. The RMS differences between the experimental data and model predictions across all simulations were excellent for both the kinematics (angles: 0.3 - 1.6 degrees, displacements: 0.1 - 0.8 mm) and kinetics (forces: 5 - 11 N, moments: 0.2 - 0.6 Nm). The validated model will be extended with physiologically realistic ligaments and utilized in surgical planning simulations.

Repeatability of a novel technique for in vivo measurement of three-dimensional patellar tracking using magnetic resonance imaging

PURPOSE

To determine the repeatability of a novel noninvasive MRI-based technique for measuring patellofemoral kinematics in vivo.

MATERIALS AND METHODS

The patellar kinematics measurement method relies on registering bone models (with associated coordinate systems) developed from a high resolution MRI scan to loaded bone positions derived from fast, low resolution MRI scans. The intrasubject variability, high resolution to low resolution registration error, and interexperimenter repeatability were quantified in experiments on three healthy subjects.

RESULTS

The intrasubject variability and registration error were within range of the accuracy of our procedure; specifically, less than or equal to 1.40 degrees for orientation and 0.81 mm for translation. The interexperimenter repeatability was less than or equal to 1.28 degrees for orientation, with the exception of patellar spin, and 0.68 mm for translation.

CONCLUSION

Our novel measurement technique can measure three-dimensional patellar tracking noninvasively during loaded flexion in a repeatable manner. Our results compare well to another noninvasive tracking protocol, fast phase-contrast MRI, which has a reported subject interexam variability of 2.4 degrees or less for patellar orientation. A particular strength of our method is that axes and high-resolution bone models need only be determined once for intrasubject comparisons. The method is sufficiently accurate and repeatable to detect clinically significant changes in patellofemoral kinematics.

Accurate assessment of patellar tracking using fiducial and intensity-based fluoroscopic techniques

Accuracies of a point-based and an intensity-based fluoroscopic methods of assessing patella tracking were determined by comparing the pattern of patellar motion with respect to orientation (flexion, internal rotation, and lateral tilt) and translation (lateral, proximal, and anterior) with the pattern of patellar motion measured using Roentgen stereophotogrammetric analysis in three cadaver knee specimens. Each pose in the patellar motion could be obtained from single as well as multiple calibrated fluoroscopic images. The errors using the intensity-based method were slightly higher than those of the point-based method, but they appear to be sufficiently low to detect clinically significant differences in patellar kinematics.

Computer-assisted distal radius osteotomy

PURPOSE

To establish the accuracy, precision, and clinical feasibility of a novel technique of computer-assisted distal radius osteotomy for the correction of symptomatic distal radius malunion.

METHODS

Six patients underwent a computer-assisted distal radius osteotomy and were followed-up for an average of 25 months. Objective radiographic measurements and functional outcomes, as measured by clinical examination including grip strength and range of motion, and Disability of the Arm, Shoulder and Hand (DASH) questionnaires, were used.

RESULTS

The mean radiographic parameters included an increase of radial inclination to 21 degrees from 12 degrees (normal, 23 degrees ). Dorsal and volar tilt (malunion) were corrected to 9 degrees from -30 degrees and 21 degrees, respectively (normal, 10 degrees ). Ulnar variance was corrected to 1.9 mm from 7.5 mm (normal, +1.5 mm). Normal is defined as the average of the contralateral limb radiographs. The mean clinical outcome measures at an average of 25 months included a DASH global score of 14, a DASH individual item average score of 1.6, and an average affected side grip strength of 79% when compared with the unaffected side.

CONCLUSIONS

The results of the computer-assisted technique were comparable with published results of traditional non-computer-assisted opening wedge osteotomy techniques. This technique allows a surgeon to accurately and precisely recognize and correct 3-dimensional deformities of the distal radius including axial malalignment (supination). The technique has the added benefit of reducing radiation exposure to the patient and surgical team because fluoroscopy is not used during the procedure. Additional benefits of the computer-assisted technique include the ability to perform multiple surgical simulations to optimize the alignment plan, and it serves as an excellent teaching tool for less-experienced surgeons.

Robust registration for computer-integrated orthopedic surgery: laboratory validation and clinical experience

In order to provide navigational guidance during computer-integrated orthopedic surgery, the anatomy of the patient must first be registered to a medical image or model. A common registration approach is to digitize points from the surface of a bone and then find the rigid transformation that best matches the points to the model by constrained optimization. Many optimization criteria, including a least-squares objective function, perform poorly if the data include spurious data points (outliers). This paper describes a statistically robust, surface-based registration algorithm that we have developed for orthopedic surgery. To find an initial estimate, the user digitizes points from predefined regions of bone that are large enough to reliably locate even in the absence of anatomic landmarks. Outliers are automatically detected and managed by integrating a statistically robust M-estimator with the iterative-closest-point algorithm. Our in vitro validation method simulated the registration process by drawing registration data points from several sets of densely digitized surface points. The method has been used clinically in computer-integrated surgery for high tibial osteotomy, distal radius osteotomy, and excision of osteoid osteoma.