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Supplemental Material for:

Spectrotemporal CT data acquisition and reconstruction at low dose

Darin Clark1, Chang-Lung Lee2, David G. Kirsch2,3, Cristian T. Badea1

Duke University Medical Center:

1Center for In Vivo Microscopy
2Departments of Radiation Oncology and 3Pharmacology and Cancer Biology

Medical Physics 42: 6317-6336, 2015

Purpose: X-ray CT is widely used, both clinically and preclinically, for fast, high-resolution, anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. We propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols.

Methods: We approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, we establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a non-linear, image domain filtration approach, we refer to as rank-sparse kernel regression, we transfer image structure from the well-sampled, time and energy averaged reconstruction to spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem, while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction sub-problems, enabling substantial undersampling. We solve the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, we apply the algorithm to study myocardial injury following radiation treatment of breast cancer.

Results: We performed quantitative, 5D simulations using the MOBY mouse phantom. 20 data sets (10 cardiac phases, 2 energies) are reconstructed with 88-micron, isotropic voxels from 450 total projections acquired over a single 360-degree rotation. In vivo, 5D cardiac injury data sets acquired in 2 mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ~60 mGy). For the simulations and the in vivo data, reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Our 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to our standard imaging protocol.

Conclusions: Our 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time.


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We ask that you provide contact information, and agree to give credit to the Duke Center for In Vivo Microscopy for any written or oral presentation using data from this site. Please use the following acknowledgement: Imaging data provided by the Duke Center for In Vivo Microscopy NIH/NIBIB (P41 EB015897).

Movies: In Vivo, 5D Reconstruction Results: Tie2Cre p53FL/+

A   B
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Supplemental movies: In vivo, 5D reconstruction results for the Tie2Cre p53FL/+ mouse (Fig. 8 in full manuscript). (A) Composite iodine (red) and gold (green) material decomposition maps overlaid on the energy-averaged reconstruction of end systole. (B) 30-slice maximum intensity projection showing all 10 phases of the cardiac cycle. Lymph nodes above the heart, which accumulate gold nanoparticles, act as positive controls for potential accumulation of gold at the site of myocardial injury. No gold accumulation is seen in the myocardium of this Tie2Cre, p53FL/+ data set. As discussed in Sec. 2.G of the full manuscript, bone appears to be composed of gold. The display windows for iodine and gold maps are scaled from 5 to 30 mg/mL. The display window for the CT data is from -500 to 2500 Hounsfield units.

Movies: In Vivo, 5D Reconstruction Results: Tie2Cre p53FL/-

A   B
scale bar
See movie directly from YouTube:   See movie directly from YouTube:
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Supplemental movies: in vivo, 5D reconstruction results for the Tie2Cre p53FL/- mouse (Fig. 10 in full manuscript). (A) Composite iodine (red) and gold (green) material decomposition maps overlaid on the energy-averaged reconstruction of end systole. (B) 30-slice maximum intensity projection showing all 10 phases of the cardiac cycle. Lymph nodes above the heart, which accumulate gold nanoparticles, act as positive controls for the potential accumulation of gold at the site of myocardial injury. As shown here and in Fig. 10 of the manuscript, significant gold accumulation is seen in the irradiated portion of myocardium of this Tie2Cre; p53FL/- data set. As discussed in Sec. 2.G of the full manuscript, bone appears to be composed of gold. The display windows for the iodine and gold maps are scaled from 5 to 30 mg/mL. The display window for the CT data is from -500 to 2500 Hounsfield units.

Comparison of regularization strategies for temporal CT reconstruction

method comparison

Reconstruction results for end diastole (1 of 10 cardiac phases) using the 2D MOBY mouse phantom1 with 180 regular angular projections, random temporal sampling, realistic spectral and noise models, and a parallel-beam geometry.

(A) Expected reconstruction result for end diastole.

(B) Time-weighted, filtered backprojection reconstruction of end diastole (see Sec. 2.C in full manuscript).

(C) Result (B) after 25 iterations of least-squares minimization using the biconjugate gradient stabilized method.2 The least-squares reconstruction was used to initialize 10 iterations of PICCS3 (prior: temporally averaged initialization), spatio-temporal TV minimization4 (equal weights for spatial and temporal gradients), and bilateral TV minimization subject to data fidelity. PICCS enforced spatial gradient sparsity and gradient sparsity relative to the prior image using a single level, piecewise-constant, B-spline tight frame transform, and soft thresholding.5 Spatio-temporal TV-enforced spatial and temporal gradient sparsity using a single level, piecewise-constant, B-spline tight frame transform and soft thresholding. Tensor products were used to incorporate the additional dimensions. Bilateral TV was minimized with rank-sparse kernel regression at a single energy (Fig. 2 in full manuscript). Equivalent regularization parameters were used for each method. Yellow arrows denote artifacts left by PICCS. Red arrows show low-frequency noise left by spatio-temporal TV. The final, average RMSE over all phases (in Hounsfield units) is shown at bottom-right of each reconstruction result. Bilateral TV outperforms PICCS and spatio-temporal TV because it enforces gradient sparsity across multiple scales of derivatives and because it copies image structure from the well-sampled temporal average image (Sec. 2.D in full manuscript).

(D) Absolute residuals for each approach. Green arrows denote roughly constant recovery of temporal resolution for all regularization methods. Intensity calibrations are as shown in Hounsfield units.

References for figure above

1 WP Segars, et al., Development of a 4-D digital mouse phantom for molecular imaging research, Mol Imag Biol 6: 149-159, 2004
2 HA Van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J Scientif Stat Comp 13:631-644, 1992
3 GH Chen, et al., Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets, Med Phys 35:660-663, 2008
4 L Ritschl, et al., Iterative 4D cardiac micro-CT image reconstruction using an adaptive spatio-temporal sparsity prior, Phys Med Biol 57:1517-1525, 2012
5 H Gao, et al., Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM), Inverse Probl 27, 2011

 

Acknowledgements:

All imaging was performed at Duke Center for In Vivo Microscopy, an NIH/NIBIB National Biomedical Technology Resource Center (P41 EB015897), with addtional support from Susan G. Komen for the Cure (IIR13263571), and an American Heart Association pre-doctoral fellowship (12PRE10290001).

 

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