3D reconstruction of a patient-specific surface model of the proximal femur from calibrated x-ray radiographs: a validation study

The accuracy of statistical shape models in predicting bone shape: A systematic review

BACKGROUND

This systematic review aims to ascertain how accurately 3D models can be predicted from two-dimensional (2D) imaging utilising statistical shape modelling.

METHODS

A systematic search of published literature was conducted in September 2022. All papers which assessed the accuracy of 3D models predicted from 2D imaging utilising statistical shape models and which validated the models against the ground truth were eligible.

RESULTS

2127 papers were screened and a total of 34 studies were included for final data extraction. The best overall achievable accuracy was 0.45 mm (root mean square error) and 0.16 mm (average error).

CONCLUSION

Statistical shape modelling can predict detailed 3D anatomical models from minimal 2D imaging. Future studies should report the intended application domain of the model, the level of accuracy required, the underlying demographics of subjects, and the method in which accuracy was calculated, with root mean square error recommended if appropriate.

Predicting Knee Joint Instability Using a Tibio-Femoral Statistical Shape Model

Statistical shape models (SSMs) are a well established computational technique to represent the morphological variability spread in a set of matching surfaces by means of compact descriptive quantities, traditionally called "modes of variation" (MoVs). SSMs of bony surfaces have been proposed in biomechanics and orthopedic clinics to investigate the relation between bone shape and joint biomechanics. In this work, an SSM of the tibio-femoral joint has been developed to elucidate the relation between MoVs and bone angular deformities causing knee instability. The SSM was built using 99 bony shapes (distal femur and proximal tibia surfaces obtained from segmented CT scans) of osteoarthritic patients. Hip-knee-ankle (HKA) angle, femoral varus-valgus (FVV) angle, internal-external femoral rotation (IER), tibial varus-valgus (TVV) angles, and tibial slope (TS) were available across the patient set. Discriminant analysis (DA) and logistic regression (LR) classifiers were adopted to underline specific MoVs accounting for knee instability. First, it was found that thirty-four MoVs were enough to describe 95% of the shape variability in the dataset. The most relevant MoVs were the one encoding the height of the femoral and tibial shafts (MoV #2) and the one representing variations of the axial section of the femoral shaft and its bending in the frontal plane (MoV #5). Second, using quadratic DA, the sensitivity results of the classification were very accurate, being all >0.85 (HKA: 0.96, FVV: 0.99, IER: 0.88, TVV: 1, TS: 0.87). The results of the LR classifier were mostly in agreement with DA, confirming statistical significance for MoV #2 (p = 0.02) in correspondence to IER and MoV #5 in correspondence to HKA (p = 0.0001), FVV (p = 0.001), and TS (p = 0.02). We can argue that the SSM successfully identified specific MoVs encoding ranges of alignment variability between distal femur and proximal tibia. This discloses the opportunity to use the SSM to predict potential misalignment in the knee for a new patient by processing the bone shapes, removing the need for measuring clinical landmarks as the rotation centers and mechanical axes.

Comparison between different screening strategies to determine the statistical shape model of the pelvises for implant design

BACKGROUND AND OBJECTIVES

The statistical shape model (SSM) of numerous bones has been used to determine the anatomical representative of the population- or race-specific design for periarticular implants. Whether to include size- and profile-mismatched bones in the SSM calculation is debatable. Therefore, the objective of this study was to characterize the screening strategies for the mismatched bones to improve the SSM calculation.

METHODS

The bone database used in this study consisted of 20 pelvises. A systematic four-staged SSM calculation was used to evaluate the accuracy of the predicted SSM shape among the four size- and profile-screening strategies. Additionally, the surface-smoothing effects on the SSM results were investigated. Two comparison indices were used in terms of profile difference and surface smoothness.

RESULTS

Significant variations in size and profile existed for the collected bones. By normalizing the aspect ratio of all bones, exclusion of the size-mismatched bones reduced the maximum and root mean square (RMS) error values of the profile difference by 18.9% and 17.5%, respectively. After further excluding the profile-improper bones, normalization reduced the RMS profile difference by 24.1% compared with the non-normalized strategy. Exclusion of the size-improper bones for non-normalized strategy would have reduced the RMS profile difference by 15.4%. After smoothness, the RMS profile difference of SSM was only 6.1% higher than that of the non-smoothness SSM.

CONCLUSIONS

The four-stage calculation showed that the most favorable strategy was to normalize bones to the same aspect ratio and exclude improperly shaped bones. The model permitted inclusion of the original characteristics of the bones and preserved their shapes and excluded only significantly improper bones. After SSM calculation, the smoothed process provided satisfaction in quality with a statistically insignificant loss in bone morphology for population- or race-specific designs of implants.

Pair-wise vs group-wise registration in statistical shape model construction: representation of physiological and pathological variability of bony surface morphology

Statistical shape models (SSM) of bony surfaces have been widely proposed in orthopedics, especially for anatomical bone modeling, joint kinematic analysis, staging of morphological abnormality, and pre- and intra-operative shape reconstruction. In the SSM computation, reference shape selection, shape registration and point correspondence computation are fundamental aspects determining the quality (generality, specificity and compactness) of the SSM. Such procedures can be made critical by the presence of large morphological dissimilarities within the surfaces, not only because of anthropometrical variability but also mainly due to pathological abnormalities. In this work, we proposed a SW pipeline for SSM construction based on pair-wise (PW) shape registration, which requires the a-priori selection of the reference shape, and on a custom iterative point correspondence algorithm. We addressed large morphological deformations in five different bony surface sets, namely proximal femur, distal femur, patella, proximal fibula and proximal tibia, extracted from a retrospective patient dataset. The technique was compared to a method from the literature, based on group-wise (GW) shape registration. As a main finding, the proposed technique provided generalization and specificity median errors, for all the five bony regions, lower than 2 mm. The comparative analysis provided basically similar results. Particularly, for the distal femur that was the shape affected by the largest pathological deformations, the differences in generalization, specificity and compactness were lower than 0.5 mm, 0.5 mm, and 1%, respectively. We can argue the proposed pipeline, along with the robust correspondence algorithm, is able to compute high-quality SSM of bony shapes, even affected by large morphological variability.

Review of 2-D/3-D Reconstruction Using Statistical Shape and Intensity Models and X-Ray Image Synthesis: Toward a Unified Framework

Patient-specific three-dimensional (3-D) bone models are useful for a number of clinical applications such as surgery planning, postoperative evaluation, as well as implant and prosthesis design. Two-dimensional-to-3-D (2-D/3-D) reconstruction, also known as model-to-modality or atlas-based 2-D/3-D registration, provides a means of obtaining a 3-D model of a patient's bones from their 2-D radiographs when 3-D imaging modalities are not available. The preferred approach for estimating both shape and density information (that would be present in a patient's computed tomography data) for 2-D/3-D reconstruction makes use of digitally reconstructed radiographs and deformable models in an iterative, non-rigid, intensity-based approach. Based on a large number of state-of-the-art 2-D/3-D bone reconstruction methods, a unified mathematical formulation of the problem is proposed in a common conceptual framework, using unambiguous terminology. In addition, shortcomings, recent adaptations, and persisting challenges are discussed along with insights for future research.

A dynamic model-based approach to motion and deformation tracking of prosthetic valves from biplane x-ray images

PURPOSE

Transcatheter aortic valve replacement (TAVR) is a minimally invasive procedure in which a prosthetic heart valve is placed and expanded within a defective aortic valve. The device placement is commonly performed using two-dimensional (2D) fluoroscopic imaging. Within this work, we propose a novel technique to track the motion and deformation of the prosthetic valve in three dimensions based on biplane fluoroscopic image sequences.

METHODS

The tracking approach uses a parameterized point cloud model of the valve stent which can undergo rigid three-dimensional (3D) transformation and different modes of expansion. Rigid elements of the model are individually rotated and translated in three dimensions to approximate the motions of the stent. Tracking is performed using an iterative 2D-3D registration procedure which estimates the model parameters by minimizing the mean-squared image values at the positions of the forward-projected model points. Additionally, an initialization technique is proposed, which locates clusters of salient features to determine the initial position and orientation of the model.

RESULTS

The proposed algorithms were evaluated based on simulations using a digital 4D CT phantom as well as experimentally acquired images of a prosthetic valve inside a chest phantom with anatomical background features. The target registration error was 0.12 ± 0.04 mm in the simulations and 0.64 ± 0.09 mm in the experimental data.

CONCLUSIONS

The proposed algorithm could be used to generate 3D visualization of the prosthetic valve from two projections. In combination with soft-tissue sensitive-imaging techniques like transesophageal echocardiography, this technique could enable 3D image guidance during TAVR procedures.

2D/3D reconstruction of the distal femur using statistical shape models addressing personalized surgical instruments in knee arthroplasty: A feasibility analysis

BACKGROUND

Personalized surgical instruments (PSI) have gained success in the domain of total knee replacement, demonstrating clinical outcomes similar or even superior to both traditional and navigated surgeries. The key requirement for prototyping PSI is the availability of the digital bony surface. In this paper, we aim at verifying whether the 2D/3D reconstruction of the distal femur, based on statistical shape models (SSM), grants sufficient accuracy, especially in the condylar regions, to support a PSI technique.

METHODS

Computed tomographic knee datasets acquired on 100 patients with severe cartilage damage were retrospectively considered in this work. All the patients underwent total knee replacement using the PSI-based surgical technique. Eighty out of 100 reconstructed distal femur surfaces were used to build the statistical model. The remaining 20 surfaces were used for testing. The 2D/3D reconstruction process was based on digital reconstructed radiographies (DRRs) obtained with a simulated X-ray projection process. An iterative optimization procedure, based on an evolutionary algorithm, systematically morphed the statistical model to decrease the difference between the DRR, obtained by the original CT dataset, and the DRR obtained from the morphed surface.

RESULTS

Over the 80 variations, the first ten modes were found sufficient to reconstruct the distal femur surface with accuracy. Using three DRR, the maximum Hausdorff and RMS distance errors were lower than 1.50 and 0.75 mm, respectively. As expected, the reconstruction quality improved by increasing the number of DRRs. Statistical difference (P < 0.001) was found in the 2 vs 3, 2 vs 4 and 2 vs 5 DRR, thus proving that adding just a single displaced projection to the two traditional sagittal and coronal X-ray images improved significantly the reconstruction quality. The effect of the PSI contact area errors on the distal cut direction featured a maximum median error lower than 2° and 0.5° on the sagittal and frontal plane, respectively. Statistical difference was found (P < 0.0001) in the reconstruction accuracy when comparing SSM built using pathologic with respect to non-pathologic shapes (cadavers), meaning that, to improve the patient-specific reconstruction, the morphologic anomalies, specific to the pathology, must be embedded into the SSM.

CONCLUSIONS

We showed that the X-ray based reconstruction of the distal femur is reasonable also in presence of pathologic bony conditions, featuring accuracy results similar to earlier reports in the literature that reconstructed normal femurs. This finding discloses the chance of applying the proposed methodology to the reconstruction of bony surfaces used in the PSI surgical approach.

Radiographic reconstruction of lower-extremity bone fragments: a first trial

PURPOSE

The correct rotational alignment of the proximal and the distal bone fragments is an essential step in a long-bone deformity correction process. In order to plan the deformity correction, plain radiographs are conventionally used. But as three-dimensional information of the complex situation is not available, the correct amount of rotation can only be approximated. Thus, the objective of this study was to develop a system to assess the rotational relationship between the proximal and distal fragments of a long bone (tibia or femur) based on a set of two calibrated X-ray radiographs.

METHODS

In order to robustly determine the rotational relationship of proximal and distal bone fragments, a statistical shape model-based 2D/3D reconstruction approach was employed. The resulting fragment models were used to determine the angle between its anatomical axes and the rotation around its particular axes. Two different studies were performed to evaluate the accuracy of the proposed system.

RESULTS

The accuracy of the complete system was evaluated in terms of major bone axis and in-plane rotational difference. The angle between the anatomical fragment axes could be measured with an average error of 0.33[Formula: see text] ± 0.27[Formula: see text], while an average in-plane rotational error of 2.27[Formula: see text] ± 1.76[Formula: see text]  and 2.67[Formula: see text]  ± 1.80[Formula: see text]  was found for the proximal and distal fragments, respectively. The overall mean surface reconstruction error was 0.81  ± 0.59 mm when the present technique was applied to the tibia and 1.12 ± 0.87 mm when it was applied to the femur.

CONCLUSIONS

A new approach for estimating the rotational parameters of long-bone fragments has been proposed. This approach is based on two conventional radiographs and 2D/3D reconstruction technology. It is generally applicable to the alignment of any long-bone fragments and could provide an important means for achieving accurate rotational alignment.

Prediction of in vivo knee joint kinematics using a combined dual fluoroscopy imaging and statistical shape modeling technique

Using computed tomography (CT) or magnetic resonance (MR) images to construct 3D knee models has been widely used in biomedical engineering research. Statistical shape modeling (SSM) method is an alternative way to provide a fast, cost-efficient, and subject-specific knee modeling technique. This study was aimed to evaluate the feasibility of using a combined dual-fluoroscopic imaging system (DFIS) and SSM method to investigate in vivo knee kinematics. Three subjects were studied during a treadmill walking. The data were compared with the kinematics obtained using a CT-based modeling technique. Geometric root-mean-square (RMS) errors between the knee models constructed using the SSM and CT-based modeling techniques were 1.16 mm and 1.40 mm for the femur and tibia, respectively. For the kinematics of the knee during the treadmill gait, the SSM model can predict the knee kinematics with RMS errors within 3.3 deg for rotation and within 2.4 mm for translation throughout the stance phase of the gait cycle compared with those obtained using the CT-based knee models. The data indicated that the combined DFIS and SSM technique could be used for quick evaluation of knee joint kinematics.

X-ray image calibration and its application to clinical orthopedics

X-ray imaging is one of the most commonly used medical imaging modality. Albeit X-ray radiographs provide important clinical information for diagnosis, planning and post-operative follow-up, the challenging interpretation due to its 2D projection characteristics and the unknown magnification factor constrain the full benefit of X-ray imaging. In order to overcome these drawbacks, we proposed here an easy-to-use X-ray calibration object and developed an optimization method to robustly find correspondences between the 3D fiducials of the calibration object and their 2D projections. In this work we present all the details of this outlined concept. Moreover, we demonstrate the potential of using such a method to precisely extract information from calibrated X-ray radiographs for two different orthopedic applications: post-operative acetabular cup implant orientation measurement and 3D vertebral body displacement measurement during preoperative traction tests. In the first application, we have achieved a clinically acceptable accuracy of below 1° for both anteversion and inclination angles, where in the second application an average displacement of 8.06±3.71 mm was measured. The results of both applications indicate the importance of using X-ray calibration in the clinical routine.

Principal component analysis in construction of 3D human knee joint models using a statistical shape model method

The statistical shape model (SSM) method that uses 2D images of the knee joint to predict the three-dimensional (3D) joint surface model has been reported in the literature. In this study, we constructed a SSM database using 152 human computed tomography (CT) knee joint models, including the femur, tibia and patella and analysed the characteristics of each principal component of the SSM. The surface models of two in vivo knees were predicted using the SSM and their 2D bi-plane fluoroscopic images. The predicted models were compared to their CT joint models. The differences between the predicted 3D knee joint surfaces and the CT image-based surfaces were 0.30 ± 0.81 mm, 0.34 ± 0.79 mm and 0.36 ± 0.59 mm for the femur, tibia and patella, respectively (average ± standard deviation). The computational time for each bone of the knee joint was within 30 s using a personal computer. The analysis of this study indicated that the SSM method could be a useful tool to construct 3D surface models of the knee with sub-millimeter accuracy in real time. Thus, it may have a broad application in computer-assisted knee surgeries that require 3D surface models of the knee.

Protocol for evaluation of robotic technology in orthopedic surgery

In recent years, robots have become commonplace in surgical procedures due to their high accuracy and repeatability. The Acrobot Sculptor is an example of such a robot that can assist with unicompartmental knee replacement. In this study, we aim to evaluate the accuracy of the robot (software and hardware) in a clinical setting. We looked at (1) segmentation by comparing the segmented data from Sculptor software to other commercial software, (2) registration by checking the inter- and intraobserver repeatability of selecting set points, and finally (3) sculpting (n = 9 cases) by evaluating the achieved implant position and orientation relative to that planned. The results from segmentation and registration were found to be accurate. The highest error was observed in flexion extension orientation of femoral implant (0.4 ± 3.7°). Mean compound rotational and translational errors for both components were 2.1 ± 0.6 mm and 3 ± 0.8° for tibia and 2.4 ± 1.2 mm and 4.3 ± 1.4° for the femur. The results from all processes used in Acrobot were small. Validation of robot in clinical settings is highly vital to ensure a good outcome for patients. It is therefore recommended to follow the protocol used here on other available similar products.

An integrated system for 3D hip joint reconstruction from 2D X-rays: a preliminary validation study

The acquisition of conventional X-ray radiographs remains the standard imaging procedure for the diagnosis of hip-related problems. However, recent studies demonstrated the benefit of using three-dimensional (3D) surface models in the clinical routine. 3D surface models of the hip joint are useful for assessing the dynamic range of motion in order to identify possible pathologies such as femoroacetabular impingement. In this paper, we present an integrated system which consists of X-ray radiograph calibration and subsequent 2D/3D hip joint reconstruction for diagnosis and planning of hip-related problems. A mobile phantom with two different sizes of fiducials was developed for X-ray radiograph calibration, which can be robustly detected within the images. On the basis of the calibrated X-ray images, a 3D reconstruction method of the acetabulum was developed and applied together with existing techniques to reconstruct a 3D surface model of the hip joint. X-ray radiographs of dry cadaveric hip bones and one cadaveric specimen with soft tissue were used to prove the robustness of the developed fiducial detection algorithm. Computed tomography scans of the cadaveric bones were used to validate the accuracy of the integrated system. The fiducial detection sensitivity was in the same range for both sizes of fiducials. While the detection sensitivity was 97.96% for the large fiducials, it was 97.62% for the small fiducials. The acetabulum and the proximal femur were reconstructed with a mean surface distance error of 1.06 and 1.01 mm, respectively. The results for fiducial detection sensitivity and 3D surface reconstruction demonstrated the capability of the integrated system for 3D hip joint reconstruction from 2D calibrated X-ray radiographs.

Patient-specific modelling of bone and bone-implant systems: the challenges

In the past three decades, finite element (FE) modelling has provided considerable understanding to the area of musculoskeletal biomechanics. However, most of this understanding has been generated using generic, standardised or idealised models. Patient-specific modelling (PSM) is almost never used for making clinical decisions. Imaging technologies have made it possible to create patient-specific geometries and FE meshes for modelling. While these have brought us closer to PSM, several challenges associated with the definition of material properties, loads, boundary conditions and interaction between components still need to be overcome. This study reviews the current status of PSM with respect to defining material behaviour and prescribing boundary conditions and interactions. With regard to the constitutive modelling of bone, it is seen that imaging is being increasingly used to define elastic properties (isotropic as well as anisotropic). However, the post-elastic and time-dependent behaviour, important for several modelling situations, is mostly obtained from in vitro experiments. Strain-based plasticity, not commonly available in FE codes, appears to have the potential of reducing an element of patient-specificity in modelling the yielding behaviour of bone. PSM of real boundary conditions that include muscles and ligaments continues to remain a challenge; many clinically relevant questions can be, however, answered without their inclusion. Simulation techniques to undertake PSM of interactions between bone and uncemented implants are available. Interference fit employed in both joint replacement fracture treatments induces considerable preload whose inclusion in models is important for the prediction of interface behaviour.

Mathematical representation of the normal proximal human femur: Application in planning of cam hip surgery

Precise modelling of the proximal femur can be used for detecting and planning corrective surgery for subjects with deformed femurs using robotic technology or navigation systems. In this study, the proximal femoral geometry has been modelled mathematically. It is hypothesised that it is possible to fit a quadratic surface or combinations of them onto different bone surfaces with a relatively good fit. Forty-six computed tomography datasets of normal proximal femora were segmented. A least-squares fitting algorithm was used to fit a quadratic surface on the femoral head and neck such that the sum of distances between a set of points on the femoral neck and the quadratic surface was minimised. Furthermore, the position of the head–neck articular margin was also measured. The femoral neck was found to be represented as a good fit to a hyperboloid with an average root mean-squared error of 1.0 ± 0.13 mm while the shape of the femoral articular margin was a reproducible sinusoidal wave form with two peaks. The mathematical description in this study can be used for planning corrective surgery for subjects with cam-type femoroacetabular impingement.

Construction of 3D human distal femoral surface models using a 3D statistical deformable model

Construction of 3D geometric surface models of human knee joint is always a challenge in biomedical engineering. This study introduced an improved statistical shape model (SSM) method that only uses 2D images of a joint to predict the 3D joint surface model. The SSM was constructed using 40 distal femur models of human knees. In this paper, a series validation and parametric analysis suggested that more than 25 distal femur models are needed to construct the SSM; each distal femur should be described using at least 3000 nodes in space; and two 2D fluoroscopic images taken in 45° directions should be used for the 3D surface shape prediction. Using this SSM method, ten independent distal femurs from 10 independent living subjects were predicted using their 2D plane fluoroscopic images. The predicted models were compared to their native 3D distal femur models constructed using their 3D MR images. The results demonstrated that using two fluoroscopic images of the knee, the overall difference between the predicted distal femur surface and the MR image-based surface was 0.16±1.16 mm. These data indicated that the SSM method could be a powerful method for construction of 3D surface geometries of the distal femur.

2D-3D shape reconstruction of the distal femur from stereo X-ray imaging using statistical shape models

Three-dimensional patient specific bone models are required in a range of medical applications, such as pre-operative surgery planning and improved guidance during surgery, modeling and simulation, and in vivo bone motion tracking. Shape reconstruction from a small number of X-ray images is desired as it lowers both the acquisition costs and the radiation dose compared to CT. We propose a method for pose estimation and shape reconstruction of 3D bone surfaces from two (or more) calibrated X-ray images using a statistical shape model (SSM). User interaction is limited to manual initialization of the mean shape. The proposed method combines a 3D distance based objective function with automatic edge selection on a Canny edge map. Landmark-edge correspondences are weighted based on the orientation difference of the projected silhouette and the corresponding image edge. The method was evaluated by rigid pose estimation of ground truth shapes as well as 3D shape estimation using a SSM of the whole femur, from stereo cadaver X-rays, in vivo biplane fluoroscopy image-pairs, and an in vivo biplane fluoroscopic sequence. Ground truth shapes for all experiments were available in the form of CT segmentations. Rigid registration of the ground truth shape to the biplane fluoroscopy achieved sub-millimeter accuracy (0.68mm) measured as root mean squared (RMS) point-to-surface (P2S) distance. The non-rigid reconstruction from the biplane fluoroscopy using the SSM also showed promising results (1.68mm RMS P2S). A feasibility study on one fluoroscopic time series illustrates the potential of the method for motion and shape estimation from fluoroscopic sequences with minimal user interaction.

Current progress in patient-specific modeling

We present a survey of recent advancements in the emerging field of patient-specific modeling (PSM). Researchers in this field are currently simulating a wide variety of tissue and organ dynamics to address challenges in various clinical domains. The majority of this research employs three-dimensional, image-based modeling techniques. Recent PSM publications mostly represent feasibility or preliminary validation studies on modeling technologies, and these systems will require further clinical validation and usability testing before they can become a standard of care. We anticipate that with further testing and research, PSM-derived technologies will eventually become valuable, versatile clinical tools.