Synopsis

Keywords: Liver, DSC & DCE Perfusion

Respiratory motion can impair the accurate estimation of physiological parameters in DCE-MR of the liver. A Deep learning network is proposed to quantitatively investigate the impact of respiratory motion on the estimation of physiological parameter maps. The proposed network provides quantitative parameters for DCE-MR and uncertainty estimates for these parameters. Here we could show that the estimated epistemic uncertainty of k_trans is sensitive to motion. This could provide important information about how well motion correction worked and how reliable the obtained quantitative DCE parameters are.

INTRODUCTION

DCE-MRI enables to quantitatively measure tissue perfusion and microvascular parameters, which serve as biomarkers in oncology ^1,2. The quantification of perfusion parameters is usually performed by analysis of the concentration time curves (CTCs)³. However, the analysis of the temporal enhancement pattern of a tissue is challenged by respiratory motion during the acquisition of T1-weighted images at different time points^4,5. This affects the accuracy of physiological parameter estimation as the motion induces variation in the signal intensity curve of a voxel. Several motion correction techniques have been proposed in the literature. However, the quantitative evaluation of the performance of motion correction method is a challenge. We propose a deep learning network to quantitatively evaluate the effect of motion correction on physiological parameter estimation by estimating not just the quantitative parameters but also the associated uncertainties.

METHODS

Simulated Data
High quality 3D DCE-MR data in the liver is difficult to acquire due to motion. Hence, CTCs were simulated by applying the extended Tofts (eTofts) model (equation 1)⁶ on physiological parameters, $$$\theta = \{k_{trans}, ve$$$ and $$$vp\}$$$. $$$k_{trans}$$$ is the volume transfer constant from the blood plasma to extravascular extracellular space (EES), $$$ve$$$ is the fractional volume of interstitial space, $$$vp$$$ is the fractional plasma volume. $$$C(t)$$$ and $$$C_p(t)$$$ are tissue and plasma concentration curves, respectively.
$$C(t) = v_pC_p(t) + k_{trans}\int_{0}^{t} \ C_p(t^\prime-\Delta t) e^{-(\frac{k_{trans}}{v_e})(t-t^{\prime}-\Delta t)} dt^{\prime} $$
Gaussian noise was added and this simulated data was used for training a deep learning (DL) network.
In-vivo Data

We applied the trained network to the DCE-MR data of a patient with hepatic tumors to evaluate parameter estimation on motion corrected and uncorrected images. The DCE-MR images were acquired continuously during free breathing for a duration of 5 minutes. A bolus of 0.01 mmol/kg of hepato-specific contrast agent (gadoxeate disodium) was administered during the acquisition. For the motion corrected images, a motion‐corrected image reconstruction method was applied ⁴.
Deep learning (DL) network
The architecture of the DL network employs a Bayesian neural network with six fully connected layers. The network transforms the CTCs into physiological parameters of the eTofts model and their associated aleatoric and epistemic uncertainties for each voxel. Aleatoric uncertainty is the inherent ambiguity in the data and cannot be reduced by increasing the size of the training data^{7, 8}. Epistemic uncertainty arises from a mismatch between the data distribution used for training (e.g. without motion artefacts) and the distribution of data used during application (e.g. with motion artefacts).
ROI analysis
We chose seven ROIs within tumors for the motion corrected and uncorrected data separately, because respiratory motion can lead to a shift of the anatomy compared to the corrected data. The parameter estimates and relative epistemic uncertainties of these regions were investigated to evaluate the effect of motion.

RESULTS

Figure 1 shows an exemplary DCE-MR slice of a liver for motion corrected and uncorrected data. The estimated physiological parameters and relative epistemic uncertainty maps of each parameter for motion corrected and uncorrected images are shown in Figure 2 and Figure 3, respectively. Tumors are characterized by high $$$k_{trans}$$$ and $$$vp$$$ and low $$$ve$$$ values. The epistemic uncertainties for motion uncorrected data increased especially in tumor regions for $$$k_{trans}$$$ as shown in Figure 3. The arrows show the increase in the epistemic uncertainty in corresponding regions of tumor for the motion corrected and uncorrected data. Figure 4a,b shows the different ROIs selected for tumor for motion corrected and uncorrected data, respectively. $$$k_{trans}$$$ was 39.59 ± 32.16% higher for the motion corrected than the uncorrected data. $$$ve$$$ was smaller by 24.85 ± 10.57% for the motion corrected than the uncorrected data with p-value <0.001. In addition, the epistemic uncertainty for $$$k_{trans}$$$ increased by 15.13 ± 11.18% when motion was not corrected. The epistemic uncertainty for $$$ve$$$ was also statistically significant different between corrected and uncorrected data but the difference was very small (10.30 ± 7.13%). There was no significant difference for parameter and uncertainty estimate of $$$vp$$$ (p-value >0.05) in both motion corrected and uncorrected data.

DISCUSSION

The physiological parameter maps for motion uncorrected data illustrated the impact of motion, which led to an underestimation of $$$k_{trans}$$$ and overestimation of $$$ve$$$, especially for small tumors⁴. In the motion uncorrected images, the epistemic uncertainty increased due to motion. Motion altered the shape of the CTCs and because the network was not trained with motion impaired data, the epistemic uncertainty increased. In particular, this was shown with an increase in the epistemic uncertainty of $$$k_{trans}$$$ in regions of tumors for motion uncorrected data. Unlike $$$ve$$$ and $$$vp$$$, $$$k_{trans}$$$ was more sensitive to motion.

CONCLUSION

This work for the first time demonstrated a link between uncertainty estimates obtained by DL and motion artefacts for DCE-MR of the liver. Motion correction improved estimation of the physiological parameters in the liver. This is confirmed by the additional epistemic uncertainty estimates which provided sensitive markers for motion artefacts.

Acknowledgements

We would like to acknowledge funding from German Research Foundation, project number GRK2260, BIOQIC.