Sequential-Scanning Dual-Energy CT Imaging Using High Temporal Resolution Image Reconstruction and Error-Compensated Material Basis Image Generation

In sequential-scanning contrast-enhanced DECT, data sets corresponding to two different tube potentials are acquired separately. Since the concentration of iodinated contrast agent in the imaged subject varies over time, sequentially scanned data sets acquired at two tube potentials are temporally inconsistent. As existing material basis image reconstruction approaches for DECT assume that the data sets acquired at two tube potentials are temporally consistent, the violation of this assumption results in inaccurate quantification accuracy of material concentration and much degraded image quality.

To address the technical challenge induced by temporal inconsistency of sequentially scanned data sets and improve quantification accuracy of material concentration in sequential-scanning contrast-enhanced DECT, in this work, we developed sequential-scanning contrast-enhanced DECT imaging using high temporal resolution image reconstruction and error-compensated material basis image generation, ACCELERATION in short.

ACCELERATION first reconstructs several time-resolved images, each corresponding to an improved temporal resolution and lower temporal-averaging error, to resolve the temporal variation of the imaged subject using the short-scan data acquired at the first tube potential. Then, ACCELERATION resolves the temporal variation of the imaged subject using the short-scan data acquired at the second tube potential. The imaged subject corresponding to the selected reference time can be obtained via temporally extrapolating the time-resolved images corresponding to the first and second tube potentials.

To improve the quantitative accuracy and image quality of material basis images, material concentration can be quantified at the reference time using the pair of calculated temporally consistent images at two tube potentials and the developed error-compensated material basis image generation technique. The error-compensated material basis image generation models the degradation process into the forward model to train the generator using the data acquired for each individual subject. The degradation process includes the beam hardening effect due to polychromatic spectrum and structural error in the dual-energy images obtained from the developed high temporal resolution image reconstruction plus temporal extrapolation. Via properly modeling the degradation process, the forward model can maximally approximate the obtained dual-energy images, such that, the structural error in the obtained dual-energy images can be compensated for the improvement of accuracy in the obtained material basis images.

The innovation in ACCELERATION is summarized as follows:

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  It achieves sequential-scanning dual-energy CT for contrast-enhanced imaging;

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  It mitigates temporal inconsistency in terms of concentration of iodinated contrast agent;

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  It explicitly models the degradation process into the forward model of the material basis image generation to properly compensate the structural error in the dual-energy images obtained from the developed high temporal resolution image reconstruction plus temporal extrapolation;

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  It explicitly leverages the measured data of each individual subject to guarantee the accuracy of temporal matching and material basis image reconstruction for each individual subject.

In this work, we demonstrated that, a low-cost sequential-scanning data acquisition scheme to implement DECT has been achieved for contrast-enhanced imaging using the developed ACCELERATION technique. Results shown in this paper demonstrated the improvement of quantification accuracy and image quality using ACCELERATION.

Our goal is to address the technical challenge induced by temporal inconsistency of sequentially scanned data sets and improve quantification accuracy of material concentration in sequential-scanning DECT. The developed ACCELERATION includes two major techniques: (i) temporal matching using high temporal resolution image reconstruction and temporal extrapolation and (ii) material quantification using error-compensated material basis image generation. The temporal matching technique addresses the technical challenge induced by temporal inconsistency of sequentially scanned data sets in sequential-scanning DECT. The error-compensated material basis image generation improves material quantification accuracy and image quality of material basis images.

To make the subject temporally consistent, one has to first resolve the temporal variation of the subject using the data acquired at one of the tube potentials. To achieve this purpose, we developed a subject-specific deep time-resolved image representation to resolve the temporal variation of the subject during the time window to acquire the data at one of the tube potentials. The imaged subject corresponding to the selected reference time can be obtained via temporally extrapolating the time-resolved images corresponding to the data acquired at two tube potentials. To improve the quantitative accuracy and image quality of material basis images, material concentration can be quantified at the selected reference time using the pair of calculated temporally consistent images at two tube potentials and the developed error-compensated material basis image generation network. Fig. 1 shows the overall framework of ACCELERATION.

For a system with a fixed gantry rotation speed, the only way to improve its temporal resolution is to use data acquired over a narrower angular range that violates the data sufficiency condition. For FBP, the data sufficiency condition specifies the minimal angular range as the short-scan angular range. Severe data-insufficiency-induced errors (a.k.a. limited view artifacts), can be observed using FBP from the data acquired over shorter than the short-scan range. Model-based iterative image reconstruction approaches leveraging prior image and sparsity [9], the low rankness of the spatial-temporal image matrix [10, 11] can be applied to reconstruct the entire imaged object without severe data-insufficiency-induced errors using a data sub-set acquired over up to one-fourth of the short-scan range. The four-dimensional digital subtraction angiography method reconstructs a three-dimensional image volume from the data acquired at a single projection view [12] using both a pre-contrast scan (the one without contrast injection) and a post-contrast scan (the one with contrast injection). By incorporating the prior knowledge of the periodicity of the data-insufficiency-induced errors, eSMART-RECON further improves temporal resolution to 4-7.5 fps [13]. To leverage the prior knowledge of the periodicity, eSMART-RECON requires that the acquired data set covers at least four scans (i.e. two forward scans plus two backward scans). By recasting the temporal resolution improvement task as a temporal extrapolation task, AIRPORT [14] improves the temporal resolution to 40 fps, the time window needed to acquire a single projection view data using a typical C-arm CBCT and the data acquired over the short-scan range.

CT image reconstruction using data acquired from a limited view range violates the data sufficiency condition and hence results in images with severe limited view artifacts unless appropriate regularization can be incorporated to constrain the otherwise ill-posed problem. However, it remains a technical challenge to appropriately design the regularization for better solving the limited view image reconstruction problem. Inappropriate regularization may lead to degraded quantitative accuracy (such as biased CT values) and/or image quality (degraded image sharpness, unnatural noise texture, image artifacts etc.).

Instead of solving the CT value for each individual image voxel, one can also represent the image-to-be-reconstructed as a deep convolutional neural network [15, 16, 17] or a deep fully connected network [18, 19, 20, 21, 22, 23, 24] with learnable parameters to regularize the image reconstruction problem using the architecture of the deep neural network. The network parameters can then be determined by best fitting the forward model of the image estimation to the measured data corresponding to a limited view range. After training the network using the data corresponding to the imaged subject, the deep neural networks with fully connected layers learns a smooth mapping from the image voxel coordinates domain to the corresponding intensity value domain. As the smoothness has been implicitly enforced from one image voxel to other nearby voxels, CT image noise and artifacts can be effectively mitigated in the reconstructed image represented by the learned smooth mapping, such that, CT image reconstruction problems under nonideal data acquisition conditions can be effectively solved. The high temporal resolution image reconstruction using deep neural networks with fully connected layers includes two steps: prior image embedding (see in Fig. 1 (b). ①) and limited view image reconstruction (see in Fig. 1 (b). ②).

Suppose that scanning at the first tube potential is performed during $[0,T_{2}]$, the tube potential is changed during $[T_{2},T_{4}]$, and scanning at the second tube potential is performed during $[T_{4},T_{6}]$. The variation of iodine concentration of the imaged subject underwent intravenous contrast injection at each image voxel can be approximately considered as general Gamma-Variate functions [25] over a relatively long duration (normally longer than 30 seconds). Given the short duration of data acquisition (e.g. about 0.2 seconds to acquire a short-scan data set using a state-of-the-art multi-detector-row CT scanners), the variation of iodine concentration and CT attenuation values within such short duration can be legitimately assumed as linear variation.

Based on the $T$ time-resolved CT images obtained by solving Eq. (2), for each voxel in the image, a linear least squares fitting is used to find a linear representation of the temporal variation of intensity value at the given image voxel. CT images corresponding to $T_{3}$ (the midpoint of $[T_{2},T_{4}]$) and the first tube potential can then be determined by linear extrapolation of each linear representation of the temporal variation of intensity value at the each image voxel corresponding to time-resolved images during $[0,T_{2}]$. Similarly, CT images corresponding to $T_{3}$ and the second tube potential can then be determined by linear extrapolation of each linear representation of the temporal variation of intensity value at the each image voxel corresponding to time-resolved images during $[T_{4},T_{6}]$. Then, temporal inconsistency in CT images corresponding to both the first and the second tube potentials are maximally mitigated at $T_{3}$. Material quantification can then be performed to obtain quantitative material concentration using the above extrapolated dual-energy images at $T_{3}$.

Through the developed high temporal resolution image reconstruction and temporal extrapolation, we can obtain CT images at two tube potentials with the nearly consistent iodine concentration, which can be used for material quantification. Due to the instability of material quantification, structural errors in the reconstructed dual-energy CT images obtained from high temporal resolution image reconstruction plus temporal extrapolation developed in Sec. II-B and Sec. II-C will be greatly amplified [26], resulting in erroneous material basis images.

To mitigate the errors in the material basis image, in this paper, instead of applying conventional image-domain material quantification procedure to obtain material basis images, an error-compensated material basis image generation network, EC-Net, has been designed and properly trained to improve quantitative accuracy and image quality of material basis images for each individual subject. The error-compensated material basis image generation models the degradation process into the forward model to train the generator using the data acquired for each individual subject. The degradation process includes the beam hardening effect due to polychromatic spectrum and structural error in the dual-energy images obtained from the developed high temporal resolution image reconstruction plus temporal extrapolation. Via properly modeling the degradation process, the forward model can maximally approximate the obtained dual-energy images, such that, the structural error in the obtained dual-energy images can be properly compensated to further improve the accuracy of the obtained material basis images.

EC-Net is trained to learn the subject-specific material quantification mapping including two sub-mappings $\mathcal{G}\circ\mathcal{D}$. Here $\mathcal{G}$ denotes the material basis image generation mapping from randomly sampled noise image to ideal material basis images. $\mathcal{D}$ denotes the dual-energy CT image degradation mapping from ideal material basis images to dual-energy CT images from the developed high temporal resolution image reconstruction plus temporal extrapolation. The material basis image generation mapping $\mathcal{G}_{\mathbf{\Phi}}$ is learned for each subject individually to maximally avoid the generalizability error induced by a model trained using a relative large data cohort. The dual-energy CT image degradation mapping $\mathcal{D}_{\mathbf{\Psi}}$, on the other hand, can be trained using a relative large data cohort to represent the features of structural errors represented in a large group of dual-energy CT images. To implement this idea, model parameters $\mathbf{\Psi}$ are determined by solving the following problem using a relatively large training data set and will be frozen during the training of the material basis image generation mapping $\mathcal{G}_{\mathbf{\Phi}}$.

The optimization problem for determining $\mathbf{\Psi}$ can be formulated as follows:

where $\hat{\mathbf{x}}_{L}$ and $\hat{\mathbf{x}}_{H}$ denote the simulated dual-energy CT images using ideal material basis images at the low and high tube potentials respectively, $\tilde{\mathbf{x}}_{L}$ and $\tilde{\mathbf{x}}_{H}$ denote the reconstructed dual-energy CT images using the high temporal resolution image reconstruction and temporal extrapolation developed in Sec. II-B and Sec. II-C respectively.

The optimization problem for determining $\mathbf{\Phi}$ can be formulated as follows:

where $\mathbf{n}$ denotes the random values sampled from the uniform distribution. Once the material basis image generation mapping has been trained for each individual subject, the optimal material basis images can be obtained via $\mathcal{G}_{\mathbf{\Phi}^{*}}(\mathbf{n})$.

$\mathcal{S}$ represents the operator for synthesizing DECT images showing as follows:

where $\hat{\mathbf{Y}}$ denotes the modeled dual-energy post-log sinogram data, $\Omega_{k^{{}^{\prime}},e}$ denotes the normalized photon number corresponding to $k^{{}^{\prime}}$-th tube potential at the $e$-th energy index, $b_{k,e}$ denotes the mass attenuation coefficient of $k$-th basis material at $e$-th energy index, $\mathbf{a}_{i,j}$ denotes $i$-, $j$-th element of the system matrix $\mathbf{A}$, $\mathbf{a}^{+}_{i,j}$ denotes $i$-, $j$-th element of $\mathbf{A}^{+}$ which represents the pseudo inverse of $\mathbf{A}$. Here we used the standard FBP algorithm to implement $\mathbf{A}^{+}$.

All our experimental implementations are based on PyTorch, and the differentiable forward projection operators in neural network are based on LEAP in [27]. All computations were performed on a workstation equipped with an Intel(R) Xeon(R) Platinum 8160 CPU @ 2.10GHz and an RTX 3090 GPU with 24GB of memory.

In addition to numerical simulations studies, in vivo human subject studies have been conducted to further demonstrate the technical feasibility of ACCELERATION. Data sets of one human subject (male, 44 years old) acquired with an institutional review board approval and written informed consent at Shanghai Jiading Central Hospital were retrospectively analyzed. The data were acquired using a MDCT system (uCT 960+, United Imaging Healthcare, Shanghai, China). Both the data acquisition and contrast agent injection protocols were approved by the institution. Projection data were processed with the needed data correction using the proprietary software toolkit provided by the vendor.

In the high temporal resolution reconstruction phase, we selected FBP, SIRT [28], PICCS [9], and SMART [10] as baseline methods. We provided the SIRT, PICCS, and SMART methods with the same prior image as the initial images for iteration as used in the proposed method, and the same projection selection method and CT image reconstruction frame count were used for fair comparison. We optimized the hyperparameters of the baseline methods as much as possible under our imaging conditions. In PICCS, $\lambda_{1}$ was set to 0.91, and $\lambda_{2}$ was set to 0.09. In SMART, singular values greater than 5% of the maximum singular value were retained. Other hyperparameters for each method were set according to the recommendations in the reference articles. In the material quantification phase, we introduced the direct inversion method [26] after FBP reconstruction of DECT images and direct inversion with the proposed high temporal resolution reconstruction and temporal extrapolation to demonstrate the effectiveness of the proposed workflow.

The normalized root mean square error (nrMSE) was used to quantitatively assess the similarity between the reconstructed image and the ground truth.

where $x_{i}$ is the pixel value of the reconstructed image, $y_{i}$ is the pixel value of the ground truth image, and $N$ is the total number of pixels, and the denominator is the root mean square value of the ground truth image. Additionally, we subtracted 1000 mg/ml from the water basis image to amplify the nrMSE, thereby more effectively reflecting the error between the reconstructed water basis image and the ground truth.

Results generated from human subject studies were also used to assess the overall qualitative image quality for imaged objects with complex anatomy and realistic temporal dynamics. Direct material quantification without and with HTR and temporal extrapolation were used as the baseline methods and the results were shown in the first and second columns of Fig. 9. ACCELERATION images are shown in the third row of the figure. As demonstrated by the figure, intensity values of iodinated vessels in the obtained water basis images are mitigated using ACCELERATION while other baseline methods cannot. As shown in the figure, iodinated vessels are erroneously enhanced in the water basis image using HRT and direct inversion (the second column of the figure). The image-domain direct inversion cannot produce accurate water basis image partially because the direct inversion does not incorporate the full X-ray spectrum into the physical forward model of the material decomposition process. Note that, in Fig. 9, the material basis images of baseline methods (No Extrapolation and HTR + Extrapolation + Direct Inversion) were reconstructed using in-house implementation. It is necessary to emphasize that the in-house implementation of these baseline methods is different from the reconstruction algorithms implemented in the commercial workstation provided by the vendor.

This work has several potential limitations which need further investigations in future studies.

First, there is no proprietary hyperparameter to control the trade-off between reconstruction accuracy and noise level of the reconstructed images in HTR or EC-Net. To control the trade-off, one must empirically stop the optimization process at an early stage. The immediate future work is to develop a new optimization framework to solve the optimization problem of HTR and EC-Net with theoretical convergence, explicit hyperparameters to control the trade-off between reconstruction accuracy and noise level, and other flexibilities to obtain imaging-task-specific image quality control.

Second, the data acquisition and contrast injection protocol in the human subject study presented in the paper were not designed and optimized for time-resolved angiography imaging task. To apply ACCELERATION to this imaging task, the data acquisition and contrast injection protocols such as the injection rate, volume and concentration of contrast agent, the rate and volume of saline chasing, the timing of data acquisition, etc., need to be specifically optimized to maximally benefit from ACCELERATION for the time-resolved angiography imaging task.

Third, the performance of HTR depends on the detailed implementation of data classification, $\{S_{t}\}$, and the selection of the number of time frames, $T$, in Eq. (2). Currently, empirical implementations of $\{S_{t}\}$ and $T$ have been applied in solving Eq. (2). The immediate future work is to systematically investigate the performance dependence of the quantitative accuracy of the reconstructed time-resolved images on different implementations of $\{S_{t}\}$, $T$, or the combination of both of them.

Fourth, the sensitivity and specificity of ACCELERATION in resolving temporal dynamics induced by realistic diseases are under investigation. In our future studies, we will rely on in vivo animal studies involving stroke models with different severity levels to systematically show the potential clinical benefits of ACCELERATION.

In this work, it has been demonstrated that using ACCELERATION, a low-cost sequential-scanning data acquisition scheme to implement DECT has been achieved for contrast-enhanced imaging. Results shown in this paper demonstrated the improvement of quantification accuracy and image quality using ACCELERATION.