An Iterative Least Squares Method for Proton CT Image Reconstruction

A stopping criterion for iterative proton CT image reconstruction based on correlated noise properties

BACKGROUND

Whereas filtered back projection algorithms for voxel-based CT image reconstruction have noise properties defined by the filter, iterative algorithms must stop at some point in their convergence and do not necessarily produce consistent noise properties for images with different degrees of heterogeneity.

PURPOSE

A least-squares iterative algorithm for proton CT (pCT) image reconstruction converges toward a unique solution for relative stopping power (RSP) that optimally fits the protons. We present a stopping criterion that delivers solutions with the property that correlations of RSP noise between voxels are relatively low. This provides a method to produce pCT images with consistent noise properties useful for proton therapy treatment planning, which relies on summing RSP along lines of voxels. Consistent noise properties will also be useful for future studies of image quality using metrics such as contrast to noise ratio, and to compare RSP noise and dose of pCT with other modalities such as dual-energy CT.

METHODS

With simulated and real images with varying heterogeneity from a prototype clinical proton imaging system, we calculate average RSP correlations between voxel pairs in uniform regions-of-interest versus distance between voxels. We define a parameter r, the remaining distance to the unique solution relative to estimated RSP noise, and our stopping criterion is based on r falling below a chosen value.

RESULTS

We find large correlations between voxels for larger values of r, and anticorrelations for smaller values. For r in the range of 0.5-1, voxels are relatively uncorrelated, and compared to smaller values of r have lower noise with only slight loss of spatial resolution.

CONCLUSIONS

Iterative algorithms not using a specific metric or rationale for stopping iterations may produce images with an unknown and arbitrary level of convergence or smoothing. We resolve this issue by stopping iterations of a least-squares iterative algorithm when r reaches the range of 0.5-1. This defines a pCT image reconstruction method with consistent statistical properties optimal for clinical use, including for treatment planning with pCT images.

Comparative accuracy and resolution assessment of two prototype proton computed tomography scanners

BACKGROUND

Improving the accuracy of relative stopping power (RSP) in proton therapy may allow reducing range margins. Proton computed tomography (pCT) has been shown to provide state-of-the-art RSP accuracy estimation, and various scanner prototypes have recently been built. The different approaches used in scanner design are expected to impact spatial resolution and RSP accuracy.

PURPOSE

The goal of this study was to perform the first direct comparison, in terms of spatial resolution and RSP accuracy, of two pCT prototype scanners installed at the same facility and by using the same image reconstruction algorithm.

METHODS

A phantom containing cylindrical inserts of known RSP was scanned at the phase-II pCT prototype of the U.S. pCT collaboration and at the commercially oriented ProtonVDA scanner. Following distance-driven binning filtered backprojection reconstruction, the radial edge spread function of high-density inserts was used to estimate the spatial resolution. RSP accuracy was evaluated by the mean absolute percent error (MAPE) over the inserts. No direct imaging dose estimation was possible, which prevented a comparison of the two scanners in terms of RSP noise.

RESULTS

In terms of RSP accuracy, both scanners achieved the same MAPE of 0.72% when excluding the porous sinus insert from the evaluation. The ProtonVDA scanner reached a better overall MAPE when all inserts and the body of the phantom were accounted for (0.81%), compared to the phase-II scanner (1.14%). The spatial resolution with the phase-II scanner was found to be 0.61 lp/mm, while for the ProtonVDA scanner somewhat lower at 0.46 lp/mm.

CONCLUSIONS

The comparison between two prototype pCT scanners operated in the same clinical facility showed that they both fulfill the requirement of an RSP accuracy of about 1%. Their spatial resolution performance reflects the different design choices of either a scanner with full tracking capabilities (phase-II) or of a more compact tracker system which only provides the positions of protons but not their directions (ProtonVDA). This article is protected by copyright. All rights reserved.

A comparison of proton stopping power measured with proton CT and x-ray CT in fresh postmortem porcine structures

PURPOSE

Currently, calculations of proton range in proton therapy patients are based on a conversion of CT Hounsfield units of patient tissues into proton relative stopping power. Uncertainties in this conversion necessitate larger proximal and distal planned target volume margins. Proton CT can potentially reduce these uncertainties by directly measuring proton stopping power. We aim to demonstrate proton CT imaging with complex porcine samples, to analyze in detail three-dimensional regions of interest, and to compare proton stopping powers directly measured by proton CT to those determined from x-ray CT scans.

METHODS

We have used a prototype proton imaging system with single proton tracking to acquire proton radiography and proton CT images of a sample of porcine pectoral girdle and ribs, and a pig's head. We also acquired close in time x-ray CT scans of the same samples and compared proton stopping power measurements from the two modalities. In the case of the pig's head, we obtained x-ray CT scans from two different scanners and compared results from high-dose and low-dose settings.

RESULTS

Comparing our reconstructed proton CT images with images derived from x-ray CT scans, we find agreement within 1% to 2% for soft tissues and discrepancies of up to 6% for compact bone. We also observed large discrepancies, up to 40%, for cavitated regions with mixed content of air, soft tissue, and bone, such as sinus cavities or tympanic bullae.

CONCLUSIONS

Our images and findings from a clinically realistic proton CT scanner demonstrate the potential for proton CT to be used for low-dose treatment planning with reduced margins.