Introduction

Nonalcoholic fatty liver disease (NAFLD) may cause different liver disease, including liver fibrosis, liver cirrhosis and nonalcoholic steatohepatitis^1,2. Assessing NAFLD severity using dynamic contrast enhanced MRI (DCE-MRI) was proposed in a recent study which applied two-compartment kinetic modeling method³. Kinetic modeling is known to suffer from the delay and dispersion induced quantification errors, and depends on the choice of AIF. In this study, we propose to apply a recently developed flow quantification method, quantitative transport mapping (QTM)⁴, to NAFLD grading. We validate QTM in a vasculature flow simulation and compare its performance in NAFLD grading on a rat DCE-MRI dataset.

Methods

QTM Algorithm: We use the transport equation to model the transport of tracers⁴:
$$\partial _{t} c(\xi,t)=-\nabla\cdot c(\xi,t) u(\xi) \qquad (1)$$
where $$$c(\xi,t)$$$ is the tracer concentration in a voxel $$$\xi$$$,$$$\nabla$$$the spatial gradient, and $$$u(\xi)$$$ the average velocity in that voxel. Rewriting Eq.1 as $$$A\overrightarrow u = \overrightarrow b$$$ , where A is a large sparse matrix, $$$\overrightarrow u$$$ a large vector concatenating $$$u(\xi)$$$ for all voxels, and $$$\overrightarrow b$$$ a large vector concatenating $$$c(\xi,t)$$$ for all voxels and all time points. The inverse problem of reconstructing the velocity field $$$\overrightarrow u$$$ is formulated as a constrained minimization problem:
$$\overrightarrow u = argmin_{\overrightarrow u} ||A\overrightarrow u-\overrightarrow b||_{2}^{2}+\lambda||\nabla \overrightarrow u||_{1} \qquad (2)$$
An L1 regularization is added in Eq.2 for denoising with $$$\lambda=10^{-3}$$$ chosen empirically according to minimal mean square error with respect to the ground truth for the simulation and image quality and L-curve characteristics for the in vivo data.
Numerical simulation: The vascular network acquired from a previous study⁵ is shown in Figure 1a, where the red segments represents the aorta and blue segments represents portal vein. The flow inside and outside the vessel network is simulated based on Poiseuille's law and Darcy’s law, respectively⁵. Tracer propagation is then simulated based on the transport equation. Simulated flow (shown in Figure 1c) and tracer concentration profile are then down-sampled to $$$[0.5,0.5,0.5] mm^3$$$, consistent with MRI imaging parameters (see below). QTM method is applied to the simulated tracer concentration profile and the reconstructed velocity map is compared with the ground truth velocity map.
In vivo DCE-MRI: 18 rat liver DCE-MRI scans (5 NAFLD grade3, 13 untreated control) were acquired using a T1-weighted 3D MRI sequence before and after the injection of gadolinium contrast agent using the following parameters: $$$[0.5,0.5,0.5] mm^3$$$ voxel size, 512x512x36 matrix, 5.6 s temporal resolution, and 60 time points. The DCE 4D image data was converted to gadolinium concentration ([Gd]) data by assuming a linear relationship between signal intensity change and contrast agent concentration⁶. QTM (Eq.2) was applied on the resulting concentration maps. The velocity amplitude of each voxel was calculated as:
$$|u(\xi)|=\sqrt {(u^x(\xi))^2+(u^y(\xi))^2+(u^z(\xi))^2} \qquad (3)$$

For comparison, the arterial blow flow ($$$LBF_a$$$ ), the portal venous blood flow ($$$LBF_v$$$ ), and the extravascular space volume ($$$V_e$$$) were computed based on a dual-input one compartment exchange model⁷:
$$\partial_t c(\xi,t)=LBF_a(\xi)c_a(t)+LBF_v(\xi)c_v(t)-\frac{(LBF_a(\xi)+LBF_v(\xi))}{V_e(\xi)}c(\xi,t) \qquad (4)$$
Here $$$c_a(t)$$$ and $$$c_v(t)$$$ are artery and portal vein input function, respectively. Statistical analysis was performed on the perfusion parameters averaged in a region of interest (ROI).

Results:

The reconstructed velocity from the simulated tracer concentration profile is shown in Figure 1d. Compared with the ground truth, QTM velocity showed good accuracy (rRMSE=0.27, linear regression $$$R^2$$$ =0.80). QTM velocity map,$$$LBF_a$$$ ,$$$LBF_v$$$ and $$$V_e$$$ map of a grade 3 NAFLD and a control case are shown in Figures 2 and 3, respectively. Only the QTM velocity showed a significant difference between NAFLD grade 3 and untreated control group (Figure 4 and 5).

Discussion and Conclusion:

QTM can reconstruct the liver blood flow with good accuracy in a numerical simulation. Compared with kinetic modeling, QTM showed the highest diagnostic accuracy for assessing NAFLD based on DCE-MRI data. Future work may include adding compartment modeling to QTM and applying QTM in human NAFLD assessment.

Acknowledgements

We don't have acknowledgements.