Polyenergetic Known-Component Reconstruction without Prior Shape Models

Abstract

Purpose:

Previous work has demonstrated that structural models of surgical tools and implants can be integrated into model-based CT reconstruction to greatly reduce metal artifacts and improve image quality. This work extends a polyenergetic formulation of known-component reconstruction (Poly-KCR) by removing the requirement that a physical model (e.g. CAD drawing) be known a priori, permitting much more widespread application.

Methods:

We adopt a single-threshold segmentation technique with the help of morphological structuring elements to build a shape model of metal components in a patient scan based on initial filtered-backprojection (FBP) reconstruction. This shape model is used as an input to Poly-KCR, a formulation of known-component reconstruction that does not require a prior knowledge of beam quality or component material composition. An investigation of performance as a function of segmentation thresholds is performed in simulation studies, and qualitative comparisons to Poly-KCR with an a priori shape model are made using physical CBCT data of an implanted cadaver and in patient data from a prototype extremities scanner.

Results:

We find that model-free Poly-KCR (MF-Poly-KCR) provides much better image quality compared to conventional reconstruction techniques (e.g. FBP). Moreover, the performance closely approximates that of Poly- KCR with an a prior shape model. In simulation studies, we find that imaging performance generally follows segmentation accuracy with slight under- or over-estimation based on the shape of the implant. In both simulation and physical data studies we find that the proposed approach can remove most of the blooming and streak artifacts around the component permitting visualization of the surrounding soft-tissues.

Conclusion:

This work shows that it is possible to perform known-component reconstruction without prior knowledge of the known component. In conjunction with the Poly-KCR technique that does not require knowledge of beam quality or material composition, very little needs to be known about the metal implant and system beforehand. These generalizations will allow more widespread application of KCR techniques in real patient studies where the information of surgical tools and implants is limited or not available.

I. INTRODUCTION

Metal artifacts associated with implants and surgical tools continue to be a problem for both diagnostic CT and interventional cone-beam CT. So-call “blooming” artifacts and streaking can significantly degrade image quality – often in the exact diagnostic region of interest (e.g. in the assessment of implant placement, loosening over time, etc.). Many strategies have been proposed to mitigate metal artifacts. Most techniques seek to replace projection data associated with metal implants with interpolated data,¹ inpainting,² or even prior image information.³ Unfortunately, this replacement can eliminate important image content in the immediate vicinity of the implant.

Recent work⁴ on known-component reconstruction (KCR) techniques have shown that integration of a shape model within a model-based reconstruction can eliminate “blooming” and streak artifacts around the metal implants, and provide good visualization right up to the boundary of the implant. Variants of KCR that use polyenergetic models for the component (Poly-KCR) have been able to re-cast the estimation problem as a joint optimization that solves for both the attenuation image as well as a spectral characterization of the components⁵ – eliminating the need for precise knowledge of the material composition of the component and the spectral quality of the x-ray beam. While this generalization is important, there are many clinical cases where shape models of the implanted components are not available. In our work, we remove this requirement by leveraging threshold-based segmentation techniques on initial FBP reconstructions to estimate the shape of metallic objects and using these estimates as inputs to a Poly-KCR reconstruction.

II. THEORETICAL AND EXPERIMENTAL METHODS

In the following sections we briefly review the Poly-KCR approach and the methodology used for estimating component shape from initial FBP images. Following that introduction, we present simulation and physical data studies used to evaluate this new processing and reconstruction approach.

2.1. Polyenergetic Known Component Reconstruction (Poly-KCR)

In this work, we leverage the Poly-KCR approach ^5,6 that jointly estimates energy-dependence due to known components and the reconstruction of background anatomy. This approach considers a factored forward model where attenuation due to the background anatomy is characterized by a monoenergetic Beer’s law and x-rays passing through the known component are modeled to include spectral effects. This model presumes that spectral effects are dominated by x-rays passing through the metal components. This model is written as

$$\overline{y}=\mathbf{D}\left\{g\right\}\exp \left(-\mathbf{A}{\mu }_{*}\right)*f\left(\mathbf{A}{b}_I\right),$$

where $\overline{y}$ denotes the mean measurement for all detectors over the complete scan, the operator D{ɡ} is a diagonal matrix representing the photon influence and detector sensitivities, the system matrix A is a discretized linear projection operator, b_I denotes a binary mask which models the shape of a homogeneous known component, μ is the background volume (not including the known-component voxels). To model the energy-dependent effects, a component-dependent Spectral-Transfer-Function(STF), f relating path length of X-ray through the component is introduced. That is instead of the usual monoenergetic assumption that is linear within the exponential, we allow for a polynomial model in the exponent for x-rays propagating through the component:

$$f\left(A{b}_I\right)=\exp \left({\sum }_{\{k=1\}}^K{\kappa }_k{\left(\mathbf{A}{b}_I\right)}^k\right)),$$

where the coefficient vector κ parameterizes a particular STF based on material composition and beam quality.

With this forward projection model, we may specify the following objective function

$$\left\{{\widehat{\mu }}_{*},\widehat{\kappa },y\right\}=\mathit{argmin}L\left({\widehat{\mu }}_{*},\widehat{\kappa };y\right)-\beta R\left({\mu }_{*}\right),$$

where L is the negative log-likelihood associate with the above forward model and a noise model. A pairwise Huber roughness penalty R controls the noise-resolution trade-off with tuning parameter β. The above objective is solved iteratively using alternating separable paraboloidal surrogates updates ⁷ to the background anatomy.μ_t and iterative coordinate descent updates to the spectral transfer function coefficients k.

2.2. Single-threshold image segmentation

We seek to avoid the necessity of having an a priori shape model by constructing a component model directly via segmentation of an initial reconstruction. While many sophisticated segmentation methods have been developed, we focus on segmentation via simple thresholding. The single threshold technique is fast and straightforward for the high- contrast metal implant scenario. Specifically, after the initial FBP reconstruction, we form a binary mask based on the attenuation values in the volume – voxels above the threshold are set to be one, and below, to zero. Since many metal objects can have interior values that exhibit severe underestimation of attenuation, we fill the interior region of these masks if the component appears hollow when the true object should be solid (without interior holes). Specifically, for hole-filling we apply the MATLAB-based morphological structuring element to detect edges and fill gaps. This process can be tuned to the situation: For instance, if the edges smooth or even straight, ‘ball’ and ‘line’ are appropriate structuring elements. If more abrupt edges are present, as with pedicle screws, ‘rectangle’ or ‘diamond’ elements perform favorably. While this simple technique yields a shape estimate for the metallic object, the exact size of the object may vary based on the exact threshold that is specified. Thus, we conduct an investigation on the sensitivity to threshold and compare Poly-KCR performance versus segmentation performance.

2.3. Simulation and Physical Data Experiments

To investigate the performance of the proposed approach, studies on simulated CBCT system and real test bench system were conducted. Specific experimental details follow.

a). Reconstruction and Data Processing Parameters

All FBP reconstructions used a Hamming filter, α = 0.5 and a cut-off frequency 0.8. For all model-based approaches, we used a relatively low regularization parameter (β = 0.05~0.1), Huber regularization with.δ = 10⁻³, and 20 iterations of image and spectral coefficient updates. For segmentation, threshold values were chosen across a range empirically, and the optimal structural element type was selected to maximize the reconstruction performance.

b). Simulation Experiments

This paper introduced two phantoms for evaluation. Both use a common background that emulates different parts of human body such as soft tissue, bone, and air regions. For the first phantom, a cuboid solid component is implanted to the modified 3D phantom near the ‘bone region’ (attenuation value 0.4) perpendicular to z-direction to emulate a spine implant. In the second, a hollow cylindrical component is implanted in axial direction inside the bone region to simulate femoral nail implantation. (See Figure 4.) The size of the phantom volume is 256 × 256 × 41, with 0.5 × 0.5 × 0.5 mm voxels. We generate the simulated projections data by using factored forward model with an STF for the metal components with spectral coefficients of κ = [–0.32096,0.02687,–0.00119,0.0002,0.0000]. The system geometry emulates a flat-panel cone-beam CT with a source-to-detector distance of 1200mm and source-to- axis distance of 600mm. Projections are 1200 × 160, 0.388 × 0.388 mm square pixels, with 360 angles over 360°.

Fig. 4.

Reconstructions of patient data from the prototype extremities scanner. Significant metal artifacts are found in the FBP reconstruction while metal artifacts are largely mitigated in the MF-Poly-KCR approach. In particular MF-Poly-KCR is able to reduce streak artifacts and improve visibility near the tibial fracture.

To evaluate the performance with different thresholds, we compute RMSE between Poly-KCR reconstructions and the true phantom. We also compare the segmentation quality as a function of threshold using the RMSE between the segmented mask and the true implant mask.

c). CBCT Test Bench and Extremity Scanner Experiments

For physical CBCT data, two different datasets were investigated. First, a clinical scenario was emulated by implanting a screw into the spine of a cadaver torso and scanning the sample on a CBCT testbench. The system uses a PaxScan 4343CB flat-panel detector with 1536 × 1536 pixels, 0.278 mm pixel pitch after 2 ×.2 binning, and a 1500 mm source-to-detector distance and a 1200 mm source-to-axis distance. Projections were acquired with 360 angles over 360°. Reconstructions were performed on a 1100 × 1200 × 200 volume with 0.25 × 0.25 × 0.25 mm voxels. In this case, a CAD model for the implant was available so that a comparison between the model-known and model-free versions of Poly-KCR may be compared.

A second dataset was obtained using a prototype extremities scanner detailed in ⁸. This prototype scanner uses a flat-panel detector with 0.278 mm pixel pitch and 600 projections views. Patient data was acquired at 90 kVp and approximately 12 mGy dose. Reconstructions used a simple correction based on the assumption of a constant scatter fraction and a 500 × 500 × 250 volume with 0.3 × 0.3 × 0.3 mm voxels. The scanned patient had a tibial shaft fracture with an intramedullary nail fixation. This component was metallic with unknown composition and without an a prior shape model.

III. RESULTS AND BREAKTHROUGH WORK

3.1. Simulation Results

Reconstruction results of both FBP and model-free Polyenergetic KCR from the simulation experiments are shown in Figure 1. For the cuboid implant, dark streaks and bright “blooming” artifacts around the component are apparent in FBP reconstruction. These are mitigated by the model-free Poly-KCR approach across a range of thresholds, though some mild artifacts remain. For the emulated orthopedic nail, blooming artifacts contaminate the boney region and the attenuation values in the rod interior. The proposed model-free Poly-KCR (MF-Poly-KCR) was able to mitigate these effects. We also present the RMSE of reconstructed image relative to true and the RMSE between the estimated component mask and true component as a function of threshold in Figure 2. As is shown in the figure, imaging performance and segmentation accuracy do not reach the peak at the same threshold, though the peaks are fairly close to each other. We note that for the cuboid implant, the optimal threshold for imaging is higher than that of the optimal threshold for segmentation accuracy. This suggests, that it is advantageous for imaging to slightly underestimate the size of this particular implant. The opposite is true for the rod-shaped implant where a slight overestimation of the size of the implant has an advantage, suggesting that the thresholding strategy is somewhat dependent on shape. Optimal thresholds (based on RMSE) are highlighted in red in Figure 1 for both implants.

Fig. 1.

Illustration of sensitivity to component model accuracy in two simulated phantoms emulating (a) a cuboid implant; and (b) an orthopedic nail. The ground truth, FBP reconstruction, and MF-Poly-KCR reconstructions over a range of segmentation threshols (mm⁻¹) are shown. The red square shows the optimal results in terms of RMSE in the background.

Fig. 2.

Comparison of imaging and segmentation performance as a function of threshold for the two simulation phantoms: a) cuboid implant, and b) hollow orthopedic nail implant. Note that the imaging optimum is not coincident with the segmentation optimum. A higher threshold is optimal for the cuboid implant suggesting that it is better to underestimate the size of the component for imaging while a lower threshold is optimal for the rod-shaped implant.

3.3. CBCT Test Bench and Extremity Scanner Results

Reconstructions of the cadaveric torso using three different methods are shown in Figure 3. FBP displays dramatic metal artifacts around the pedicle screw, making it difficult to assess placement and visualize surrounding tissues. In contrast, Poly-KCR (with an a priori shape model) improves the image quality significantly by removing blooming artifacts and most of the streak artifacts. MF-Poly-KCR achieves nearly the same results as Poly-KCR, except for some mild residual shading effects around the screw. Several thresholds were investigated (in the range 0.055–0.064 mm⁻¹, with a 0.001 mm⁻¹ interval). However, they do not vary remarkably, suggesting that precise selections of threshold are not required.

Fig. 3.

A comparison of reconstruction methods for flat-panel CBCT data of an implanted cadaver. While significant metal artifacts are present in the FBP reconstruction, blooming and streak artifacts are greatly reduced in the proposed model-free Poly-KCR approach. Moreover, the image quality approaches that of the Poly-KCR approach where a CAD model was used to inform the model-based reconstruction.

Reconstructions from the extremities dataset are shown in Figure 4. Similar to other studies the metal intramedullary nail is sufficiently large to produce significant streak artifacts (most evident in the axial images) in the FBP reconstruction. Streaking and blooming artifacts decrease visibility in the vicinity of the nail including the fracture region making healing assessments more difficult. In contrast, the MF-Poly-KCR approach is able to largely mitigate metal artifacts despite not knowing the shape or material composition of the implant.

IV. DISCUSSION and CONCLUSION

This paper describes a model-free polyenergetic KCR which is an extension of previous work on KCR. Specifically, we perform a pre-segmentation strategy to generate a shape mode of the “known” component even though a shape model is not known a priori. In combination with a Poly-KCR approach that also does not require beam quality and energy-dependent system characterizations, we find that the proposed method outperforms the conventional reconstruction techniques and approximates the performance of Poly-KCR with a priori shape models. This work greatly broadens the applicability of KCR methods since most prior knowledge assumptions have been eliminated. We still presume that components are homogeneous in material composition and that spectral effects are dominated by the metal implant. However, such assumptions are sufficient to apply the data to clinical datasets like the tibial fracture illustrated in this work. By relaxing the requirements for prior knowledge of the implant there is great potential to apply the MF-Poly-KCR approach across a range of clinical applications to help mitigate metal artifacts in computed tomography.