Iterative image reconstruction with polar coordinate discretized system matrix for optical CT radiochromic gel dosimetry

BACKGROUND

Gel dosimeters are a potential tool for measuring the complex dose distributions that characterize modern radiotherapy. A prototype tabletop solid-tank fan-beam optical CT scanner for readout of gel dosimeters was recently developed. This scanner does not have a straight raypath from source to detector, thus images cannot be reconstructed using filtered backprojection (FBP) and iterative techniques are required. Iterative image reconstruction requires a system matrix that describes the geometry of the imaging system. Stored system matrices can become immensely large, making them impractical for storage on a typical desktop computer.

PURPOSE

Here we develop a method to reduce the storage size of optical CT system matrices through use of polar coordinate discretization while accounting for the refraction in optical CT systems.

METHODS

A ray tracing simulator was developed to track the path of light rays as they traverse the different mediums of the optical CT scanner. Cartesian coordinate discretized system matrices (CCDSMs) and polar coordinate discretized system matrices (PCDSMs) were generated by discretizing the reconstruction area of the optical CT scanner into a Cartesian pixel grid and a polar coordinate pixel grid, respectively. The length of each ray through each pixel was calculated and used to populate the system matrices. To ensure equal weighting during iterative reconstruction, the radial rings of PCDSMs were asymmetrically spaced such that the area of each polar pixel was constant. Two clinical phantoms and several synthetic phantoms were produced and used to evaluate the reconstruction techniques under known conditions. Reconstructed images were analyzed in terms of spatial resolution, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal nonuniformity (SNU), and Gamma map pass percentage.

RESULTS

A storage size reduction of 99.72% was found when comparing a PCDSM to a CCDSM with the same total number of pixels. Images reconstructed with a PCDSM were found to have superior SNR, CNR, SNU, and Gamma (1 mm, 1%) pass percentage compared to those reconstructed with a CCDSM. Increasing spatial resolution in the radial direction with increasing radial distance was found in both PCDSM and CCDSM reconstructions due to the outer regions refracting light more severely. Images reconstructed with a PCDSM showed a decrease in spatial resolution in the azimuthal directions as radial distance increases, due to the widening of the polar pixels. However, this can be mitigated with only a slight increase in storage size by increasing the number of projections. A loss of spatial resolution in the radial direction within 5 mm radially from center was found when reconstructing with a PCDSM, due to the large innermost pixels. However, this was remedied by increasing the number of radial rings within the PCDSM, yielding radial spatial resolution on par with images reconstructed with a CCDSM and a storage size reduction of 99.26%.

CONCLUSIONS

Discretizing the image pixel elements in polar coordinates achieved a system matrix storage size reduction of 99.26% with only minimal reduction in the image quality.

Fast method for computing a system matrix using a polar-coordinate pixel model with concentric annuluses of different radial widths

Despite better reconstruction quality for incomplete or noisy projection data compared to analytic reconstruction, computed tomography iterative techniques are time-consuming, mainly due to high system matrix computation. A polar-coordinate pixel model with concentric annuluses of different radial widths was established and a fast method for computing the system matrix was presented based on characteristics of this model. Compared with the Siddon algorithm and an efficient Cartesian algorithm introduced by Zhang, the proposed algorithm based on the simultaneous algebraic reconstruction technique shows speed advantages for both numerical simulation and experiment, without noticeable loss of image quality.

Contribution of perfusion to the 11 C-acetate signal in brown adipose tissue assessed by DCE-MRI and 68 Ga-DOTA PET in a rat model

PURPOSE

Determine if dynamic contrast enhanced (DCE) -MRI and/or 68 gallium 1,4,7,10-tetraazacyclododecane N, N', N″, N‴-tretraacetic acid (⁶⁸ Ga-DOTA) positron emission tomography (PET) can assess perfusion in rat brown adipose tissue (BAT). Evaluate changes in perfusion between cold-stimulated and heat-inhibited BAT. Determine if the ¹¹ C-acetate pharmacokinetic model can be constrained with perfusion information to improve assessment of BAT oxidative metabolism.

METHODS

Rats were split into three groups. In group 1 (N = 6), DCE-MRI with gadobutrol was compared directly to ⁶⁸ Ga-DOTA PET following exposure to 10 °C for 48 h. ¹¹ C-Acetate PET was also performed to assess oxidation. In group 2 (N = 4), only ⁶⁸ Ga-DOTA PET was acquired following exposure to 10 °C for 48 h. Finally, in group 3 (N = 10), perfusion was assessed with DCE-MRI in rats exposed to 10 °C or 30 °C for 48 h, and oxidation was measured with ¹¹ C-acetate. Perfusion was quantified with a two-compartment pharmacokinetic model, while oxidation was assessed by a four-compartment model.

RESULTS

DCE-MRI and ⁶⁸ Ga-DOTA PET provided similar perfusion measures, but a decrease in the perfusion signal was noted with longer imaging sessions. Exposure to 10 °C or 30 °C did not affect the perfusion measures, but the ¹¹ C-acetate signal increased in BAT at 10 °C. Without prior information about blood volume, the ¹¹ C-acetate compartment model overestimated blood volume and underestimated oxidation in 10 °C BAT.

CONCLUSION

Precise assessment of oxidation via ¹¹ C-acetate PET requires prior information about blood volume which can be obtained by DCE-MRI or ⁶⁸ Ga-DOTA PET. Since perfusion can change rapidly, simultaneous PET-MRI would be preferred.

System matrix computation vs storage on GPU: A comparative study in cone beam CT

PURPOSE

Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersection distances between the trajectories of photons and the object, also called ray tracing or system matrix computation. This work focused on the thin-ray model is aimed at comparing different system matrix handling strategies using graphical processing units (GPUs).

METHODS

In this work, the system matrix is modeled by thin rays intersecting a regular grid of box-shaped voxels, known to be an accurate representation of the forward projection operator in CT. However, an uncompressed system matrix exceeds the random access memory (RAM) capacities of typical computers by one order of magnitude or more. Considering the RAM limitations of GPU hardware, several system matrix handling methods were compared: full storage of a compressed system matrix, on-the-fly computation of its coefficients, and partial storage of the system matrix with partial on-the-fly computation. These methods were tested on geometries mimicking a cone beam CT (CBCT) acquisition of a human head. Execution times of three routines of interest were compared: forward projection, backprojection, and ordered-subsets convex (OSC) iteration.

RESULTS

A fully stored system matrix yielded the shortest backprojection and OSC iteration times, with a 1.52× acceleration for OSC when compared to the on-the-fly approach. Nevertheless, the maximum problem size was bound by the available GPU RAM and geometrical symmetries. On-the-fly coefficient computation did not require symmetries and was shown to be the fastest for forward projection. It also offered reasonable execution times of about 176.4 ms per view per OSC iteration for a detector of 512 × 448 pixels and a volume of 384³ voxels, using commodity GPU hardware. Partial system matrix storage has shown a performance similar to the on-the-fly approach, while still relying on symmetries.

CONCLUSION

Partial system matrix storage was shown to yield the lowest relative performance. On-the-fly ray tracing was shown to be the most flexible method, yielding reasonable execution times. A fully stored system matrix allowed for the lowest backprojection and OSC iteration times and may be of interest for certain performance-oriented applications.