Material Decomposition from Photon-Counting CT using a Convolutional Neural Network and Energy-Integrating CT Training Labels

Abstract

Objective.

Photon-counting CT (PCCT) has better dose efficiency and spectral resolution than energy-integrating CT, which is advantageous for material decomposition. Unfortunately, the accuracy of PCCT-based material decomposition is limited due to spectral distortions in the photon-counting detector (PCD).

Approach.

In this work, we demonstrate a deep learning (DL) approach that compensates for spectral distortions in the PCD and improves accuracy in material decomposition by using decomposition maps provided by high-dose multi-energy-integrating detector (EID) data as training labels. We use a 3D U-net architecture and compare networks with PCD filtered backprojection (FBP) reconstruction (FBP2Decomp), PCD iterative reconstruction (Iter2Decomp), and PCD decomposition (Decomp2Decomp) as the input.

Main results.

We found that our Iter2Decomp approach performs best, but DL outperforms matrix inversion decomposition regardless of the input. Compared to PCD matrix inversion decomposition, Iter2Decomp gives 27.50% lower root mean squared error (RMSE) in the iodine (I) map and 59.87% lower RMSE in the photoelectric effect (PE) map. In addition, it increases the structural similarity (SSIM) by 1.92%, 6.05%, and 9.33% in the I, Compton scattering (CS), and PE maps, respectively. When taking measurements from iodine and calcium vials, Iter2Decomp provides excellent agreement with multi-EID decomposition. One limitation is some blurring caused by our DL approach, with a decrease from 1.98 line pairs/mm at 50% modulation transfer function (MTF) with PCD matrix inversion decomposition to 1.75 line pairs/mm at 50% MTF when using Iter2Decomp.

Significance.

Overall, this work demonstrates that our DL approach with high-dose multi-EID derived decomposition labels is effective at generating more accurate material maps from PCD data. More accurate preclinical spectral PCCT imaging such as this could serve for developing nanoparticles that show promise in the field of theranostics (therapy and diagnostics).

1. Introduction

Photon counting detectors (PCDs) offer enormous potential to improve CT imaging. A PCD counts the incident photons and bins them using energy thresholds. Each threshold image records only those photons with energy greater than a user-defined threshold. Therefore, spectral CT with a PCD provides improved dose efficiency and spectral resolution compared to a conventional scan with an energy-integrating detector (EID) [1, 2]. Unfortunately, PCDs also suffer from effects such as K-escape, charge sharing, and pulse pileup that distort their spectral response [1]. These distortions make it difficult to perform accurate material decomposition in photon-counting CT (PCCT). Therefore, finding methods for improving material decomposition is critical to maximize the benefits of PCCT.

In the past, distortion reduction for a PCD has been attempted through model-based iterative inversion approaches. For instance, a paper by Ponchut describes an energy response model with a charge sharing component that can be used in iterative deconvolution to recover the incident energy spectrum from the spectrum output by a Medipix 2 PCD [3]. Others, such as Taguchi et al. [4] and Roessl et al. [5] have developed and validated mathematical models of pulse pileup that can be incorporated into iterative image reconstruction algorithms for PCCT. Dickmann et al. calibrated a multiplicative correction function for PCD projections that is designed to account for charge sharing, K-escape, and pulse pileup effects in experiments using a Dectris Santis PCD and an aluminum slab as the sample [6]. However, these conventional methods tend to be computationally expensive, numerically unstable, or very sensitive to errors in the forward model. As a result, researchers have turned to data-driven approaches.

In recent years, deep learning (DL) has become a popular way to perform distortion compensation and material decomposition in PCCT. In many prior DL approaches, the neural network was trained using data from a PCCT simulation that models distortions such as pulse pileup and charge sharing when generating projections. Abascal et al. [7] and Bussod et al. [8] took human data or realistic human phantoms, segmented them into bone and soft tissue material maps, then used a computer simulation to generate material projections, PCCT projections, and PCCT reconstructions. They then used this data to train networks for image and projection domain material decomposition [7, 8]. Likewise, others generated training data for a network that predicts material maps in the image domain or distortion-corrected projections by passing simple phantoms such as Shepp-Logan or a random triangulation into a PCCT simulation [9-11]. Use of simulation data for training offers key advantages, such as the availability of ground truth labels and the ability to generate very large training sets. However, due to the difficulty of producing a realistic PCCT simulation, a model trained on simulation data will not always be viable for real PCCT scans. Among those who used simulation data for network training, some simply showed the performance of their approach within a simulated test set [9, 10] while others demonstrated how their trained model generalizes to experimental scans [7].

Another common approach for generating training data in DL approaches is to run an experimental PCCT scan of a physical phantom with known insert concentrations. Material maps or monochromatic projections that can be used as training labels are easily generated from such a phantom [12, 13]. Although this is a convenient strategy, there may be some limitations in the ability of a network trained on a physical phantom with simple object shapes to generalize to a test set with data from real human or animal anatomy.

In this work, we use DL to compensate for spectral distortions and improve accuracy in material decomposition maps by using both PCD and EID data in network training. We performed PCCT scans of ex-vivo mice and created training labels by decomposing multi-energy scans of the same mice from an EID. After a network has been trained with these labels, it can be used to generate distortion-compensated material maps from PCD scan data without the need for corresponding EID scans. Therefore, our DL approach exploits the benefits of fast, low-dose, multi-energy scanning with a single x-ray source offered by a PCD while still generating accurate material maps. Our multi-EID data is a good source for training labels because it has very little noise due to high x-ray dose and is not affected by the spectral distortions that occur when using a PCD. Furthermore, our use of real preclinical PCD imaging data in DL training ensures that our networks will generalize well to test data in this setting.

To our knowledge, only our group has done DL material decomposition from PCD scans using multi-EID material maps as training labels. We have recently presented the idea in one SPIE conference manuscript [14] using this approach, but this prior work only tried the PCD FBP reconstruction as input to the image domain network and compared DL predictions to noisy decompositions from matrix inversion of PCD FBP reconstructions. This paper presents work that builds on that prior study by comparing our DL approach with low noise decompositions from matrix inversion of PCD iterative reconstructions and by evaluating several choices for network input.

2. Methods

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) [15]. Both the EID and PCD imaging chains use a G-297 x-ray tube (Varian Medical Systems) with 0.3 mm focal spot size and an Epsilon high-frequency x-ray generator (EMD Technologies) [15]. The x-ray beams were filtered with 0.1 mm Cu.

To provide 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 scans, 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, these helical scans were 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 roughly 8.2 times lower than the dose of 296 mGy for the 3 EID scans described above.

2.2. Image Reconstruction

The micro-CT data has been reconstructed with an isotropic voxel size of 0.125 mm using either weighted filtered back projection (FBP) [16] or an iterative reconstruction algorithm. For our iterative image reconstructions, we used the split Bregman method with the add-residual-back strategy [17] and rank-sparse kernel regression regularization (RSKR) [18], solving the following optimization problem:

$$\mathrm{X}={\text{arg min}}_X\frac{1}{2}{\sum }_e\Vert RX(e)-Y(e){\Vert }_2^2+\lambda \Vert X{\Vert }_{BTV}.$$ (1)

Thus, we solve iteratively for the vectorized, reconstructed data, the columns of X, for each energy simultaneously (indexed by e). The reconstruction for each energy minimizes the reprojection error (R, system projection matrix) relative to the log-transformed projection data acquired at each energy (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.

Each set of multi-EID scans was reconstructed using this iterative RSKR approach with 3 iterations. For each PCD micro-CT scan, we did two reconstructions: one using the iterative RSKR approach and the other using FBP with a Ram-Lak filter. After reconstructing PCD and EID images, we used the imregister function in MATLAB to compute an affine transform between imaging chains. The registration minimized mean squared error (MSE) between the EID and PCD data and operated at 1 pyramid level.

2.3. Material Decomposition

We performed image-based material decomposition on the EID and PCD iterative reconstructions using the method of Alvarez and Macovski [19]. We did not decompose the PCD FBP reconstructions because this results in material maps with very high noise levels. 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:

$$\mathrm{X}(e_i)={\mathrm{C}}_{\text{PE}}{\mathrm{M}}_{\text{PE}}(e_i)+{\mathrm{C}}_{\text{CS}}{\mathrm{M}}_{\text{CS}}(e_i)+{\mathrm{C}}_{\mathrm{I}}{\mathrm{M}}_{\mathrm{I}}(e_i).$$ (2)

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

$$C=X{M}^{-1}.$$ (3)

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 at each energy that was computed using vials of water and known concentrations of I and calcium (Ca) 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 [18].

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) [20]. Liposomal-based contrast agents containing iodine (Lip-I) were fabricated similar to methods described previously [21]. Four mice with sarcomas were intravenously injected with Lip-I (1.32 mg I/kg body weight) and were euthanized shortly thereafter. The mice were immersed in formalin for 5 days, then scanned with our PCD and multi-EID micro-CT. Both the lower and upper body were scanned. The mouse data sets contain vials of iodine solutions with concentrations of 10, 5, 2.5, 1.25, and 0.625 mg/mL, as well as a vial of calcium solution with a concentration of 50 mg/mL and a vial of water. We have also used an additional mouse with a sarcoma tumor that was injected with Lip-I (1.32 mg I/kg body weight) and imaged in vivo 5 days post injection. All animal procedures were approved by Duke University Institutional Care and Use Committee (IACUC) and adhered to the NIH Guide for the Care and Use of Laboratory Animals.

2.5. Network Training and Testing

We used five sets of matching PCD and EID micro-CT scans from four mice for network training and validation and one set from the upper body of one mouse was held out for testing. We trained three different convolutional neural networks (CNN), each with material decomposition via matrix inversion of the multi-EID iterative reconstruction as training labels and one of the following as input: 1. PCD FBP reconstruction (FBP2Decomp) 2. PCD iterative reconstruction (Iter2Decomp) 3. material decomposition via matrix inversion of the PCD iterative reconstruction (Decomp2Decomp). Figure 1 shows an example axial slice from each of these multi-EID and PCD tomographic images and their associated decomposition via matrix inversion. Note the differences in the coefficients of variations in the water vial for the PCD FBP reconstruction relative to PCD iterative reconstruction. The iterative RSKR reconstruction dramatically reduces the noise for all energies. Significant differences in the decompositions are visible between PCD matrix inversion (D) and multi-EID matrix inversion (E), particularly for I and PE maps. The vial with I concentration of 2.5 mg/mL is only visible in the multi-EID decomposition (E).

Figure 1. Example axial slices used for DL decomposition.

A) multi-EID iterative RSKR reconstruction, with vial materials and concentrations shown on 40 kVp image. B) PCD FBP reconstruction, C) PCD iterative RSKR reconstruction, D) PCD matrix inversion decomposition following iterative RSKR reconstruction, and E) multi-EID matrix inversion decomposition following iterative RSKR reconstruction. For A-C, the units of attenuation are cm⁻¹. For D-E, the units are mg/mL for I and ratio relative to water for CS and PE. Each image is labeled with its corresponding energy threshold, material, or x-ray tube voltage. Coefficient of variation (CV) measurements from the water vial show a dramatic decrease in image noise following iterative reconstruction of the PCD data (B vs. C).

We implemented a U-net CNN architecture [22] using the PyTorch library [23]. A U-net architecture with 2D convolutions has been used in several prior PCCT material decomposition papers [7, 11, 14]. Our implementation differs from this past work by using 3D convolutions, with 1 convolution at each level. The use of 3D convolutions allows the network to exploit spatial correlations in the x, y, and z directions, while having 1 convolution at each level reduced training time and helped prevent overfitting on the training set. The details of our network architecture and training procedure are in Figure 2. The network has 4 input channels for FBP2Decomp and Iter2Decomp and 3 input channels for Decomp2Decomp. Otherwise, the network architecture is identical for all 3 network input choices. The PCD reconstructions are rescaled to have mean 0 and standard deviation 1 across all energies prior to being passed into the network. The PCD decompositions that are input into the network retain their original scaling. The 3D U-net was trained using partially overlapping 3D patches (size 38 x 62 x 62, stride 26 x 50 x 50) of the 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 from multi-EID micro-CT as labels. Prior to training the 3D U-net, the order of the 3D patches from our five sets was randomly shuffled. Then, 90% of the patches were selected for training, with the remaining 10% used for validation. Since the 3D U-net 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 additional cropping operation indicated by the purple arrow in Figure 2 ensures consistent dimensions of feature maps that are being concatenated. We trained our 3D U-net using a mean squared error (MSE) loss function with a batch size of 16, Adam optimizer [24], and 1000 training epochs. For each network, we tried several values on the order of 10⁻⁴ for the initial learning rate and report results based on the learning rate that gave highest quantitative accuracy in the test set. For the FBP2Decomp and Decomp2Decomp networks, we found a value of 2 x 10⁻⁴ to be optimal. For the Iter2Decomp network, an initial learning rate of 4 x 10⁻⁴ was optimal. We implemented a learning rate scheduler that changes the learning rate by a factor of 0.5 every time the validation loss fails to decrease for 30 consecutive epochs and used early stopping to halt training if the validation loss fails to decrease for 60 consecutive epochs. Each U-net was trained on a computer running Linux with 4 Nvidia Quadro RTX 8000 GPUs. Once training was complete, we used all 3 trained networks to predict I, CS, and PE maps with partially overlapping 3D patches of PCD data from the test set as inputs.

Figure 2. Diagram of our 3D U-net architecture and training procedure.

The number of feature maps at each stage is shown in the diagram.

2.6. Performance Evaluation

We evaluated the performance of our trained 3D U-net models on the test set ex-vivo scans using both qualitative and quantitative methods. In all these comparisons, we included the material maps from multi-EID via matrix inversion as a surrogate for ground truth. Furthermore, the predicted decompositions from our 3D U-nets were compared to our current standard for PCD decomposition, matrix inversion following iterative reconstruction. For visualization purposes, we show a slice of the I, CS, and PE maps from each of the 5 decomposition approaches, as well as absolute value of the difference between multi-EID material maps and material maps from the other approaches.

For quantification of error, we measured the root mean squared error (RMSE) and mean structural similarity (SSIM) over the whole volume relative to multi-EID decomposition. In addition, we compared measurements (mean and standard deviation) from I vials in the I map and the calcium vial in the PE map for all 5 decomposition approaches. Using measurements from the I material map, we computed the contrast to noise ratio (CNR) in I vials with the following formula:

$$CNR=\frac{{\mu }_I-{\mu }_{Water}}{\sqrt{\frac{{\sigma }_I^2+{\sigma }_{Water}^2}{2}}}.$$ (4)

Where μ_I and σ_I are the mean and standard deviation from an I vial and μ_Water and σ_Water are the mean and standard deviation from a water vial. We computed the CNR for the I vials with concentrations of 5 mg/mL, 2.5 mg/mL, 1.25 mg/mL, and 0.625 mg/mL. These CNR values were assessed relative to the Rose criterion, which states that an object needs a CNR of at least 3-5 to be detected by the human eye [25].

To determine how our DL approach and different choices of network input affect spatial resolution, we acquired helical PCD and EID scans of a physical phantom with a thin tungsten wire (0.03 mm diameter) using the same settings as described in section 2.1. We generated PCD FBP reconstruction, PCD iterative reconstruction, and PCD matrix inversion decomposition results from this scan, then input each of these into the appropriate trained 3D U-net to generate material map predictions. We recomposed these 3D U-net predictions into EID images at 40 kVp, 50 kVp, and 80 kVp using a sensitivity matrix from our ex vivo mouse scans. From the recomposed 40 kVp images, we derived modulation transfer functions (MTF) by fitting a Gaussian curve to the average of horizontal, vertical, and diagonal line profiles through the wire and then taking the Fourier transform of this curve. For comparison, we derived the MTF using the same method for the PCD iterative reconstruction with threshold of 25 keV and EID iterative reconstruction at 40 kVp.

3. Results

Figure 3 shows the training and validation loss curves for each 3D U-net. Although the training was set to run for a maximum of 1000 epochs, all three networks stopped training within 750 epochs due to our early stopping criterion used in the implementation. As shown by the validation loss, the Decomp2Decomp network converged the fastest. Training took 12 hours and 29 minutes for FBP2Decomp, 8 hours and 34 minutes for Iter2Decomp, and 5 hours and 36 minutes for Decomp2Decomp. After a U-net has been trained, it takes roughly 40 seconds to use this network to generate predicted material maps from a PCD reconstruction or decomposition. On the other hand, it takes roughly 60 seconds to generate a matrix inversion decomposition using CPU implementation for a PCD reconstruction of the same size.

Figure 3.

A) Training and B) validation loss curves for all three 3D U-nets.

Figure 4 shows an axial slice of the I (red), CS (gray) and PE (green) maps of a test set from each of the decomposition approaches. We also combined the material maps for a composite visualization achieved in ImageJ. Compared to the multi-EID decomposition, the PCD iterative reconstruction followed by matrix inversion consistently underestimates I concentrations and overestimates PE values. This result is consistent with our prior observations that the CdTe-based PCD has lower Quantum Efficiency and, therefore, lower sensitivity to Iodine near its K-edge due to Cd and Te K-escape photons (peaks at ~27 keV (Cd) and 32 keV (Te)) and charge sharing between neighboring pixels [26]. All three U-net approaches reduce these biases in the I and PE maps to provide better qualitative agreement with the multi-EID decomposition.

Figure 4. Example slice from I, CS, PE, and composite material maps for each decomposition method.

A) multi-EID matrix inversion decomposition from iterative reconstruction, B) PCD matrix inversion decomposition from iterative reconstruction, C) prediction by FBP2Decomp, D) prediction by Iter2Decomp, and E) prediction by Decomp2Decomp. The 2.5 mg/mL I vial marked by a yellow rectangle is clearly visible in A) and lost in B), but recovered in C), D), and E).

Figure 5 shows measured I intensities in all 5 iodine vials as well as PE intensities from the 50 mg/mL calcium vial for all the decomposition methods. The mean measurements demonstrate that the PCD decomposition via matrix inversion underestimates the intensities in I vials and overestimates the PE value in the Ca vial relative to the multi-EID material maps. All three U-net approaches mitigate the bias in I vials. Compared to PCD decomposition, Iter2Decomp and Decomp2Decomp provide much better agreement with multi-EID in the calcium vial. This is consistent with the qualitative results from Figure 4. Overall, it appears that the Iter2Decomp network provides the best agreement with measurements from the multi-EID decomposition in I and PE maps. On the other hand, Decomp2Decomp shows the greatest tendency to overestimate iodine concentrations, while FBP2Decomp greatly underestimates the PE value from the calcium vial. Comparison of standard deviation error bars from iodine vial measurements show that all the DL predictions have lower noise level (better precision) than the PCD decomposition. One limitation is that the U-net approaches predict presence of I in the water vial (mean 0.45 mg/mL for Iter2Decomp). However, there is no apparent cross-contamination between I and PE, with all three DL approaches predicting 0 mg/mL I in the calcium vial and PE values between 0.9 and 1 in all five iodine vials. Although the U-net predictions give more accurate vial measurements than the PCD decomposition, they tend to overestimate low iodine concentrations and underestimate high iodine concentrations. One reason for this is that a network trained with mean squared error loss tends to bring predicted values closer to the average intensity.

Figure 5. Material map intensities measured in vials of known concentration.

The calcium vial intensity is measured in the PE map, and all others are measured in the I map. The height of the bar indicates mean intensity, and the error bar shows ± 1 standard deviation. Dashed horizontal lines indicate the expected iodine and PE values.

Figure 6 shows the RMSE and mean SSIM of PCD Decomposition and all three U-net approaches relative to the multi-EID decomposition. Compared to the PCD decomposition, the DL approaches show improved RMSE in I and PE maps and improved SSIM in all three material maps regardless of choice of network input. Compared to PCD matrix inversion decomposition, Iter2Decomp gives 27.50% lower RMSE in the I map and 59.87% lower RMSE in the PE map. In addition, it increases the SSIM by 1.92%, 6.05%, and 9.33% in the I, CS, and PE maps, respectively. The discrepancy between validation loss results in Figure 3B and RMSE in Figure 6A may be due to the choice of validation set. Future work with a larger training set should hold out one entire scan as a validation set.

Figure 6. A) RMSE and B) mean SSIM of I, CS, and PE material maps.

RMSE and SSIM values for PCD decomposition and all three U-net approaches are computed relative to the multi-EID decomposition.

Figure 7 shows example slices from the absolute value of difference maps between multi-EID decomposition and each of the other four decomposition approaches. This figure clearly demonstrates the ability of all three U-net approaches to reduce the effects of spectral distortions in I and PE maps. As indicated by the yellow arrows, the Iter2Decomp approach (C) shows the lowest I error, while the Decomp2Decomp approach (D) appears to be most effective in reducing PE error in highly enhancing structures such as the bone and calcium vial.

Figure 7. Absolute decomposition residuals.

Example slice from I, CS, PE, and composite maps of absolute value of difference between multi-EID matrix inversion decomposition and A) PCD matrix inversion decomposition from iterative reconstruction, B) prediction by FBP2Decomp, C) prediction by Iter2Decomp, and D) prediction by Decomp2Decomp. Note the two arrows indicating the lowest error for I in Iter2Decomp and for PE in Decomp2Decomp.

Figure 8 shows CNR values for I vials from each of our decomposition approaches. The PCD performance near the K-edge of I clearly degrades the quality of the PCD matrix inversion decomposition, with only the 5 mg/mL vial lying above the upper limit of the Rose criterion in this decomposition. Conversely, all three U-net methods increase the CNR relative to multi-EID CT for concentrations of 1.25 mg/mL and above. We acknowledge that overestimation of I concentration by the U-net methods may play a role in these results. However, the improved CNR is seen even in vials where the U-net methods give very similar or lower intensity than the multi-EID (such as 2.5 and 5 mg/mL I), which suggests that the denoising of the networks improves detectability at low concentrations for larger structures.

Figure 8. Contrast to noise ratio for each I vial.

A horizontal line indicating the upper limit of the Rose criterion for detectability (CNR=5) has been included for context.

Figure 9 shows MTF measurements from 40 kVp EID iterative reconstruction, 25 keV PCD iterative reconstruction, and recomposed 40 kVP EID images from the U-net predicted material maps. Based on this result, all three DL approaches show worse spatial resolution at 50% MTF than the 1.98 line pairs/mm in the PCD reconstruction with energy threshold of 25 keV. However, the Iter2Decomp result has the least blurring, with 1.75 line pairs/mm at 50% MTF.

Figure 9. Modulation transfer function (MTF) from lowest energy reconstruction.

40 kVp images for the U-net approaches were generated by applying a sensitivity matrix to the predicted material maps.

Finally, in Figure 10 we compare the decompositions from matrix inversion of PCD iterative reconstruction and from Iter2Decomp U-net on a mouse with a sarcoma tumor imaged in vivo 5 days post injection of Lip-I. There is a large accumulation of Lip-I in the tumor due to enhanced permeability and retention effect [27]. The Iter2Decomp method improves the visibility of the tumor on the I map and reduces contamination between the I and PE maps. This figure illustrates the usefulness of our preclinical PCCT imaging in cancer studies and in testing nanoparticle contrast agents.

Figure 10. Material decomposition in a mouse with a sarcoma tumor.

Results are shown A) using matrix inversion of PCD iterative reconstruction and B) using the Iter2Decomp U-net. Note the arrow (bottom, left) indicating the improved decomposition performance in the I vial when using the Iter2Decomp method.

4. Discussion and Conclusions

In this work, we demonstrated a supervised DL method that compensates for spectral distortions in PCCT material decompositions by using decompositions from high dose multi-EID scans as training labels. We evaluated the performance of this approach using three different options for the training input and compared them to the PCD matrix inversion decomposition. Our findings suggest that Iter2Decomp is the ideal implementation of our DL approach due to its superior performance in terms of spatial resolution and quantitative accuracy of iodine concentrations.

Each choice of training input has its unique advantages and drawbacks. A FBP2Decomp network would be ideal for high-throughput material decomposition due to the speed of FBP reconstruction. However, it may be prone to excessive blurring because of the high noise level of its input. An Iter2Decomp network will involve increased reconstruction times but may offer improved spatial resolution. Finally, the Decomp2Decomp network allows us to assess the effects of both low-noise input and distortion compensation without a change of domain from CT images to decomposition maps.

As seen in both the material maps and the absolute differences from the multi-EID decomposition, all three U-net approaches reduced the bias observed in the I and PE maps relative to PCD matrix inversion decomposition. However, measurements from vials suggest that the Iter2Decomp is the best choice. Although the Decomp2Decomp approach may be the most accurate in the calcium vial, the Iter2Decomp approach shows good agreement with the multi-EID decomposition over a wide range of iodine concentrations, which could be crucial when doing in vivo imaging with contrast agent.

In MTF plots, the Iter2Decomp shows the least severe loss of spatial resolution. This result is not surprising given our prior expectation that a lower noise reconstruction would result in less blurring.

Overall, these results reveal that a network that uses multi-EID decomposition as training labels can provide excellent performance in generating distortion-compensated material maps. The Iter2Decomp network is very well suited for this task in our current implementation. The other DL approaches also show improvement over PCD matrix inversion decomposition but may require modifications in the training procedure to achieve quantitative accuracy comparable to Iter2Decomp.

There are a few limitations that should be addressed. MTF plots showed that our DL approach gave substantially lower spatial resolution than matrix inversion decompositions from both PCD and EID data. This is likely due to the use of an MSE loss function, so future work should aim to determine if other loss functions such as gradient correlation [12, 14] can produce a network that generates distortion-compensated material decompositions while preserving high spatial frequencies. Furthermore, the issue of imperfect registration between the EID and PCD data should be considered. Although we did register the PCD and EID imaging chains, a study that trains a network with PCD and EID data from simulation, which has perfect registration, would be a valuable addition to this work for understanding these issues. Additionally, transfer learning approaches from simulated data could be also tested. Despite these areas for improvement, this work provides valuable insight into the use of supervised DL with high dose EID data for PCD distortion compensation in material maps. The approach detailed in this paper allows one to reap the benefits of low dose and fast scan time offered by a PCD while achieving more accurate material separation. Since our Lip-I nanoparticles are similar to other liposomes used for drug delivery (e.g. Doxil) [28], our imaging could serve in drug delivery studies or in developing combination therapies. In conclusion, more accurate preclinical PCCT imaging such as this could serve for developing nanoparticles that show promise in the developing field of theranostics (therapy and diagnostics).