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MOTIF-CORD: Motion Integrated Forward Model with Co-Estimated Coil Sensitivity and Regularization by Denoiser for Free Breathing Liver DCE-MRI

Chunxu Guo¹, Sihao Chen¹, Weijie Gan¹, Yuyang Hu¹, Jiaming Liu¹, Cihat Eldeniz¹, Yasheng Chen¹, Ulugbek S. Kamilov¹, Tyler J. Fraum¹, and Hongyu An¹
¹Washington University in St. Louis, St. Louis, MO, United States

Synopsis

Keywords: Image Reconstruction, Motion Correction

Motivation: Dynamic contrast-enhanced (DCE) MRI faces challenges from respiratory motion and sub-optimal DCE contrast timing. Free-breathing DCE with high temporal resolution is desirable.

Goal(s): We aim to reconstruct respiratory motion-free and high temporal resolution DCE-MRI.

Approach: We proposed a Motion Integrated Forward model using motion vector fields and jointly estimated coil sensitivity to reconstruct severely under-sampled DCE data. Furthermore, we utilized a model-based deep learning framework to amalgamate the knowledge of the measurement model and the denoising prior.

Results: The proposed method provided deformable motion vector fields, coil-sensitivity maps, and sharp motion-free DCE images without artifacts using highly under-sampled data.

Impact: This method provides good quality free-breathing liver DCE MR images with high temporal resolution. It will eliminate the need for breath-holding. Moreover, continuous acquisition and high temporal resolution reconstruction mitigate the problem of sub-optimal DCE contrast in clinical diagnosis.

Introduction

The standard-of-care (SOC) for DCE-MRI typically involves acquiring multiple breath-hold images after contrast injection ¹. Breath hold acquisition usually takes about 15-25 seconds, which is challenging for patients ^1-3. Moreover, discrete multiple post-contrast phases (e.g. arterial phase, portal venous phases, etc) are often difficult to time appropriately. Any divergence from optimal timing (i.e., too early or too late) can impact diagnosis ¹. Free-breathing DCE with continuous acquisition and high temporal DCE reconstruction provide solutions to these challenges.
The primary objective in this study is to mitigate respiratory motion artifacts and improve temporal resolution for DCE-MRI. In our study, we presented an integrated method to derive deformable motion vector field (MVF), jointly estimate coil sensitivity, and integrated motion in a physics-based deep learning reconstruction with a learned denoiser prior.

Methods

Data Acquisition and Phase Binning: A self-navigated respiratory motion detection MR sequence, CAPTURE ⁴, was used to acquire DCE images before, during, and after contrast injection. The DCE images were divided into 34 DCE contrasts with a time interval of 10 seconds, each DCE contrast data (10 seconds) were binned into 5 respiratory phases.
4D MRI and Motion Estimation: Phase2Phase (P2P) ⁵ was employed to reconstruct 4D motion-resolved MRI images from under-sampled k-space data for each DCE contrast. A registration method NODEO ⁶ was used to estimate 3D deformable MVFs from the 4D MRI images.
Image Reconstruction with Motion Correction: MOTIF-CORD is a physics model-based deep learning (MBDL) algorithm that integrates MVF and uses denoiser as a prior. Briefly, we can formulate our reconstruction as an optimization problem:
$$
\boldsymbol{x}^*=\underset{\boldsymbol{x}}{\arg \min } \ g(\boldsymbol{x})+h(\boldsymbol{x}) ,
$$
where $$$g$$$ is data consistency (DC) term and $$$h$$$ is the regularization term.
The DC is based on the forward model of MR imaging:
$$
\boldsymbol{H}_i^t=\boldsymbol{S}^t \boldsymbol{F} \boldsymbol{C}_i \boldsymbol{M}^t ,
$$
where $$$\boldsymbol{S}^t$$$ is the sampling function of phase $$$t$$$, $$$\boldsymbol{F}$$$ is the forward-Fourier (FFT) operator, $$$\boldsymbol{C}_i$$$ is the coil sensitivity for Coil $$$i$$$ which is also jointly estimated from measurements, $$$\boldsymbol{M}^t$$$ are the MVFs generated from P2P that transform phase $$$1$$$ to the target phase $$$t$$$. Then we can define our DC term:
$$
g(\boldsymbol{x})=\sum_t \sum_i \frac{1}{2}\left\|\boldsymbol{H}_i^t \boldsymbol{x}-\boldsymbol{y}_i^t\right\|_1 ,
$$
then we will define our explicit regularization term:
$$
h(\boldsymbol{x})=\frac{\tau}{2} \boldsymbol{x}^{\top}\left(\boldsymbol{x}-\mathrm{D}_\sigma(\boldsymbol{x})\right) ,
$$
where $$$\mathrm{D}_\sigma$$$ is a learned image denoiser. The gradient of the explicit regularizer has the form of:
$$
\nabla_{\boldsymbol{x}} h(\boldsymbol{x})=\tau\left(\boldsymbol{x}-\mathrm{D}_\sigma(\boldsymbol{x})\right) .
$$
The gradient of the loss function is:
$$
\mathrm{G}(\boldsymbol{x})=\nabla g(\boldsymbol{x})+\tau\left(\boldsymbol{x}-\mathrm{D}_\sigma(\boldsymbol{x})\right) .
$$
We can apply RED^7,12 variant of deep unrolling^8,9 (DU) as an optimizer, and the update step of each unrolling layer is:
$$
\boldsymbol{x}^k=x^{k-1}-\gamma \mathrm{G}\left(x^{k-1}\right).
$$
Training of Denoiser and CSM Estimator: The training was conducted using an end-to-end approach with the DU structures. A Noise2Noise¹⁰ (N2N) was employed as training strategy, which allows for training with only noisy measurements.

Results

For comparative, we selected several reconstruction methods:
MCNUFFT: Using end-of-expiration phase acquisition data, which constitutes 1/5 of the total acquired data.
Fourier-Forward¹¹ (FF): Utilizing all the acquired data. The reconstruction is based on gradient descent to minimize the DC, without integrating MVF.
MOTIF: Similar to FF, except the forward model integrates the MVF.
DL-MOTIF: Similar to MOTIF, except the loss consists of both the DC and regularizer.
MOTIF-CORD: Using all the acquired data and utilizing DU structure to optimize the loss function and jointly estimate CSMs.
As depicted in Figure 2, the reconstructed images at Contrast 4 (corresponding to the early arterial phase) are presented. MCNUFFT is characterized by streaking artifacts. Although the FF, MOTIF and DL-MOTIF method reduces these artifacts. MOTIF-SEIR presents the best result compared to previous methods.
Figure 3 presents a comparison of the estimated CSMs with the widely recognized LowK method. The difference between static and dynamic 3% LowK is to generate single set of CSMs or different CSM for each contrast. Our jointly estimated CSMs exhibit greater smoothness and resemblance to the Static 3% LowK result, particularly within the body.
Figure 4 presents the MOTIF-SEIR images across all 34 DCE contrasts from a single free-breathing DCE scan for a patient. These images provide continuous DCE contrasts. Clinical widely-used arterial, portal venous, transitional, and 5-minute delay phases are readily available from these 34 continuous DCE sets.

Conclusion

MOTIF-CORD has improved image quality and accuracy by reconstructing sharp, artifact-free and motion-free DCE-MRI images from severely under-sampled data at a 14.9% of the Nyquist sampling rate.
It corrects motion by integrating MVF and all k-space data. Furthermore, physics model based deep learning reconstruction with jointly learned coil sensitivity and denoiser prior provides high quality DCE images with a temporal resolution of 10 seconds.

Acknowledgements

This project is partly supported by funding from Siemens Healthineers.

References

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Figures

The acquired data is divided into two disjoint sets, F₁ and F₂. The DU optimizer is employed to minimize the loss between the measurements from F1 and the estimated image, denoted as f^t This estimated image undergoes a transformation via the forward model, transitioning from image space to measurement space. The training objective is the noisy measurement F₂, with the loss being weighted using the L₁ norm.

As indicated by the yellow arrow, the hepatic portal area in MCNUFFT is blurred and noisy, and the small hepatic artery, denoted by the orange arrow, is barely discernible. The FF method shows some improvement, but the image remains blurry. The MOTIF result is clearer, albeit noisy. DL-MOTIF's result is less noisy, but the portal area remains blurry. Among all, MOTIF-CORD provides the best reconstruction, with a clear portal area and great reconstruction quality for the small artery.

The first row displays the CSM estimated by the Static 3% LowK methods, clearly delineating the subject’s body boundary and the coils’ sensitivity area. The second row presents the results from the Dynamic 3% LowK, which contains substantial object structure information as opposed to coil sensitivity information. The third row features CSMs generated by the CSM estimator, exhibiting results similar to the Static 3% LowK methods, particularly within the body, while preserving the dynamic property.

This figure presents all 34 contrasts for an oncology patient. Each contrast utilizes a distinct, non-overlapping 10-second data segment.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

1884

DOI: https://doi.org/10.58530/2024/1884