Greybox: A hybrid algorithm for direct estimation of tracer kinetic parameters from undersampled DCE-MRI data

Abstract

Background: A variety of deep learning-based and iterative approaches are available to predict Tracer Kinetic (TK) parameters from fully sampled or undersampled dynamic contrast-enhanced (DCE) MRI data. However, both the methods offer distinct benefits and drawbacks.

Purpose: To propose a hybrid algorithm (named as 'Greybox'), using both model- as well as DL-based, for solving a multi-parametric non-linear inverse problem of directly estimating TK parameters from undersampled DCE MRI data, which is invariant to undersampling rate.

Methods: The proposed algorithm was inspired by plug-and-play algorithms used for solving linear inverse imaging problems. This technique was tested for its effectiveness in solving the nonlinear ill-posed inverse problem of generating 3D TK parameter maps from four-dimensional (4D; Spatial + Temporal) retrospectively undersampled k-space data. The algorithm learns a deep learning-based prior using UNET to estimate the $K_{\mathrm{trans}}$ and $V_p$ parameters based on the Patlak pharmacokinetic model, and this trained prior was utilized to estimate the TK parameter maps using an iterative gradient-based optimization scheme. Unlike the existing DL models, this network is invariant to the undersampling rate of the input data. The proposed method was compared with the total variation-based direct reconstruction technique on brain, breast, and prostate DCE-MRI datasets for various undersampling rates using the Radial Golden Angle (RGA) scheme. For the breast dataset, an indirect estimation using the Fast Composite Splitting algorithm was utilized for comparison. Undersampling rates of 8 $\times$ , 12 $\times$ and 20 $\times$ were used for the experiments, and the results were compared using the PSNR and SSIM as metrics. For the breast dataset of 10 patients, data from four patients were utilized for training (1032 samples), two for validation (752 samples), and the entire volume of four patients for testing. Similarly, for the prostate dataset of 18 patients, 10 patients were utilized for training (720 samples), five for validation (216 samples), and the whole volume of three patients for testing. For the brain dataset of nineteen patients, ten patients were used for training (3152 samples), five for validation (1168 samples), and the whole volume of four patients for testing. Statistical tests were also conducted to assess the significance of the improvement in performance.

Results: The experiments showed that the proposed Greybox performs significantly better than other direct reconstruction methods. The proposed algorithm improved the estimated $K_{\mathrm{trans}}$ and $V_p$ in terms of the peak signal-to-noise ratio by up to 3 dB compared to other standard reconstruction methods.

Conclusion: The proposed hybrid reconstruction algorithm, Greybox, can provide state-of-the-art performance in solving the nonlinear inverse problem of DCE-MRI. This is also the first of its kind to utilize convolutional neural network-based encodings as part of the plug-and-play priors to improve the performance of the reconstruction algorithm.

Keywords: K trans $\mathbf {K_{trans}}$ ; V p $\mathbf {V_{p}}$ ; AIF; DCE‐MRI; Fast‐MRI; compressive sensing; quantitative imaging.