2.1

Image Acquisition

All image data were acquired on our dual-source, micro-CT imaging system that has one EID (Dexela 1512 CMOS x-ray detector with a CsI scintillator, 75 μm pixel size) and one PCD (Dectris Santis 1604, 150 μm pixel size, 4 energy thresholds) [7]. For this study, we scanned 2 mice that were injected with soft tissue sarcomas and liposomal-based iodine contrast agent. For both PCD and EID protocols, we acquired separate ex-vivo micro-CT scans for the upper and lower body.

To perform material decomposition from multi-EID micro-CT data, we acquired three different EID scans with the following parameter settings: i) 80 kVp, 40 mA, 10 ms/exposure, ii) 50 kVp, 50 mA, 16 ms/exposure, and iii) 40 kVp, 50 mA, 16 ms/exposure. Each scan used a helical trajectory, with 900 projections over 1070 degrees rotation and 1.25 cm vertical translation.

For our PCD scan, we used an X-ray tube voltage of 80 kVp, current of 2 mA, integration time of 200 ms/exposure, and energy thresholds of 25, 34, 50, and 60 keV. Just like the EID scans, this helical scan was acquired with 900 projections, 1070 degrees rotation, and 1.25 cm vertical translation. The estimated dose for this PCD scan was 36 mGy, which is much lower than the estimated dose of 296 mGy for the 3 EID scans described above.

2.2

Image Reconstruction

For the multi-EID micro-CT data, we performed an iterative reconstruction using the split Bregman method with the add-residual-back strategy [8] and rank-sparse kernel regression regularization (RSKR) [9], solving the following optimization problem:

Thus, we solve iteratively for the vectorized, reconstructed data, the columns of X, for each energy threshold simultaneously (indexed by e). The reconstruction for each threshold minimizes the reprojection error (R, system projection matrix) relative to the log-transformed projection data acquired at each threshold (the columns of Y). To reduce noise in the reconstructed results, this data fidelity term is minimized subject to the bilateral total variation (BTV) measured within and between energies via RSKR. Unlike the multi-EID data, the PCD micro-CT images were reconstructed using filtered back projection (FBP) with a Ram-Lak filter to explore the potential of our CNN to perform denoising and material decomposition simultaneously.

2.3

Material Decomposition

We performed image-based material decomposition on the EID and PCD micro-CT reconstructions using the approach of Alvarez and Macovski [10]. We chose to decompose CT images into iodine (I), Compton scattering (CS), and photoelectric effect (PE) maps. Thus, we performed a post-reconstruction spectral decomposition with I, PE and CS as bases:

The matrix inversion spectral decomposition was performed by solving the following linear system at each voxel:

In this formulation, C is the least-squares solution for the concentration of I (mg/mL) and the fractions of PE and CS relative to water. M is a matrix of material sensitivities (attenuation/mg/mL for iodine) at each energy that was computed using vials of water and known concentrations of iodine and calcium that were included in the scans. Finally, X is the attenuation coefficient of the voxel under consideration at energy e. Orthogonal subspace projection was used to prevent negative concentrations. PCD micro-CT data was also decomposed via matrix inversion for comparison.

2.4

Animal Experiments

We used a transplant model of soft tissue sarcoma that resembles human undifferentiated pleomorphic sarcoma. A sarcoma cell line was generated from an autochthonous soft tissue sarcoma (p53/MCA model) induced in C57BL/6 wild type mice by intramuscular injection of adenovirus expressing Cas9 endonuclease and sgRNA to Trp53 gene (Adeno-sgp53-Cas9; Viraquest) followed by intramuscular injection of the carcinogen 3-methylcholenthrene (MCA) [11]. Liposomal-based contrast agents containing iodine (Lip-I) were fabricated similar to methods described previously [12]. Two mice with sarcomas were intravenously injected with Lip-I (1.32 mg I/kg body weight) and shortly after, were euthanized. The mice were immersed in formalin for 5 days, then scanned with our PCD micro-CT and multi-EID micro-CT. For this preliminary work, we used two mice with sarcomas, but more mice will be used in the near future.

2.5

Network Training and Testing

Using the Pytorch library, we implemented a CNN with a 3D U-net architecture for material decomposition. The details of network architecture [13] and our training scheme are shown in Figure 1. Three matching sets of PCD and EID micro-CT scans from two mice were used for training and one set from the upper body of one mouse was held out for testing. The CNN was trained using partially overlapping 3D patches (size 38 x 62 x 62, stride 26 x 50 x 50) from PCD micro-CT images as input and smaller (size 26 x 50 x 50, stride 26 x 50 x 50), non-overlapping 3D patches of the corresponding I, CS, and PE material maps obtained via multi-EID micro-CT as labels. Each PCD energy threshold is treated as a separate input channel. Since the CNN does not use zero padding for convolutions, it crops input patches down to the size of the labels, which prevents patch artifacts when the predicted material map patches are stitched back into a complete image. The 5 x 5 x 5 convolutions ensure consistent dimensions of feature maps that are being concatenated. We trained our CNN using a mean square error (MSE) loss function with a batch size of 32, Adam optimizer [14] with learning rate of 5 x 10^-5, and 500 training epochs. Once training was complete, we used the 3D U-net to predict I, CS, and PE maps with partially overlapping 3D patches of PCD micro-CT images from the test set as inputs.

Figure 1.

Diagram of our 3D U-net architecture and training procedure. The number of filters for each convolution operation is shown in the diagram. The network is trained using 3D patches of the PCD images as inputs and 3D patches of the multi-EID material maps as labels.

2.6

Performance Evaluation

We evaluated performance on the test set using both qualitative and quantitative methods. The material maps derived from multi-EID images via matrix inversion served as a surrogate for ground truth. For quantitative comparisons, we measured the root mean square error (RMSE) over the whole volume for PCD with matrix inversion decomposition and for 3D U-net decomposition. In addition, we compared measurements (mean and standard deviation) from I and Ca vials in the I and PE maps for all 3 decomposition approaches. For PCD with matrix inversion-based decomposition, we used the FBP reconstruction as the input because this is also what the 3D U- net takes as an input. Finally, we generated modulation transfer functions (MTF) derived from iodine maps for the EID decomposition and the 3D U-net decomposition to assess how well the CNN preserves spatial resolution.