Sirisha Tadimalla^{1}, Claudia Green^{2}, Denise Steinmann^{3}, Sascha Koehler^{4}, Hans-Paul Juretschke^{3}, Iina Laitinen^{3}, John C Waterton^{5,6}, Paul D Hockings^{7,8}, Catherine D Hines^{9}, Gunnar Schütz^{2}, and Steven Sourbron^{1}

A variety of Gadoxetate DCE-MRI models have been proposed to derive hepatocyte uptake and efflux rates in the rat, but it is unclear which provides most reliable measurements. Here, we compare four models in terms of their test-retest repeatability on 9 rats measured in 3 sites. Results indicate that a two-compartment high-flow model, assuming negligible sinusoidal backflux and a fixed population-based extracellular volume fraction, provides most repeatable measures of hepatocellular function in the healthy rat.

Data Acquisition Three sites imaged 3 rats each on Bruker MRI scanners at 4.7T (A) and 7T (B, C) using Paravision 6.0.1 (Bruker BioSpin, Ettlingen, Germany) over the course of 2 days (2-7 days apart). The scan protocol consisted of T2W images for anatomy identification and a retrospectively triggered gradient echo T1W acquisition (3D, TE/TR = 1.1/5.8 ms, FOV = 60 x 60 x 35 mm, 64 x 64 x 26 matrix, flip angle = 20˚, acquisition time = 58 sec), adapted to include 13 flip angles (range = 1-30˚) for vFA T1 mapping, and a dynamic series acquired with a single flip angle of 20˚ and 30 measurements with temporal resolution 58 sec, with 0.025 mmol/kg gadoxetate injected after 5 baselines.

Image processing
ROIs were manually drawn around liver and
spleen, and MR signal intensities were extracted from the vFA and DCE-MRI
datasets. Pre-contrast longitudinal relaxation rates (R1) were calculated and
used to determine dynamic post-contrast R1, using the signal equation of a spoiled-GRE.
Gadoxetate concentrations were calculated based on known relaxivities in the liver
and spleen^{2}.
All image processing was performed centrally using custom-written code in
MATLAB 2018a.

Gadoxetate DCE-MRI model-fitting
Four models (Models 1-4) were derived from a
unified, generic gadoxetate DCE-MRI model (Fig. 1) and used to measure kinetic
parameters (hepatocyte uptake rate, $$$k_{he}=\frac{K_{HE}}{V}$$$, sinusoidal backflux, $$$k_{eh}=\frac{K_{EH}}{V}$$$,
biliary efflux, $$$k_{bh}=\frac{K_{BH}}{V}$$$ and biliary flow, $$$F_b=\frac{F_B}{V}$$$) in rat liver. Table 1 shows liver concentrations expressed in
terms of model parameters and the assumptions applied to derive Models 1-4. Volume
fractions were normalised to total tissue volume, V. Extracellular concentration, $$$c_e(t)$$$, was derived from spleen concentrations as $$$c_e(t)=\frac{c_{spleen}(t)}{v_{e,spleen}}$$$, using a fixed $$$v_{e,spleen} = 0.43$$$.^{2,3} Least-squares model-fitting
was performed using the LMFIT^{6} package in Python 3.6 using
Levenberg-Marquardt minimization with parameter constraints - $$$v_e, v_h: (0,1)$$$ and $$$k_{he}, k_{eh}, k_{bh}, F_b: (0, 0.1)$$$.

Data analysis Test-retest repeatability was calculated as $$$\%CV=100×\frac{standard deviation(X_{day1},X_{day2})}{mean(X_{day1},X_{day2})}$$$ where $$$X = v_e, k_{he}, k_{bh}$$$ for each model. $$$\%CV$$$ was averaged over all rats. A high $$$\%CV$$$ indicates low repeatability.

Three-compartment models (1&2) provide poor
precision of biliary efflux rates, with mean values of the same order of
magnitude as the hepatocyte uptake rates, unlike those reported in literature.^{3}
These models also provide poor precision (large standard deviations) of
extracellular volume fractions and hepatocyte uptake rates. Test-retest
repeatability of extracellular volume fractions is also poor for both models. Model
1 also provides low precision of the sinusoidal backflux rates (Day 1:
0.030±0.043 and Day 2: 0.025±0.036 mL/s/mL), indicating no advantage over
Model 2.

On the other hand, the two-compartment models (3&4) provide greater precision of biliary efflux rates, with Model 4 also providing the most repeatable measures ($$$\%CV=34.7$$$). Mean values of biliary efflux rates obtained with these models are an order of magnitude lower than the hepatocyte uptake rates, as expected. Precision and repeatability of hepatocyte uptake rates are comparable across these models. While Model 3 provides a measure of the extracellular volume fraction, precision and repeatability of the measurement are low. Therefore, there is no advantage in using Model 3 over Model 4.

These results provide a compelling argument for using a population-based liver $$$v_e$$$ in studies where the normal variability of extracellular volume fraction is expected to be low, for instance, in healthy rat subjects. Future work using interventions is needed to determine the effect of changes in $$$v_e$$$ on the accuracy of parameters assessed with a model that uses a fixed $$$v_e$$$.

1. Georgiou L, Penny J, Nicholls G, et al. Modeling Gadoxetate liver uptake and efflux using dynamic contrast-enhanced magnetic resonance imaging enables preclinical quantification of transporter drug-drug interactions. Invest Radiol. 2018;53(9):563-570.

2. Ulloa JL, Stahl S, Yates J, et al. Assessment of Gadoxetate DCE-MRI as a biomarker of hepatobiliary transporter inhibition. NMR Biomed. 2013;26:1258-1270.

3. Karageorgis A, Lenhard SC, Yerby B, et al. A multi-center preclinical study of gadoxetate DCE-MRI in rats as a biomarker of drug induced inhibition of liver transporter function. PLoS ONE 2018;13(5): e0197213.

4. Giraudeau C, Leporq B, Doblas S, et al. Gadoxetate-enhanced MR imaging and compartmental modelling to assess hepatocyte bidirectional transport function in rats with advanced liver fibrosis. Eur Radiol. 2017;27:1804-1811.

5. Blouin A, Bolender RP and Weibel ER. Distribution of organelles and membranes between hepatocytes and nonhepatocytes in the rat liver parenchyma. J Cell Biol. 1977;72-441-455.

6. Newville M, Stensitzki T, Allen DB, et al. LMFIT: Non-linear least-squares minimization and curve-fitting for Python. Zenodo 2014. http://doi.org/10.5281/zenodo.11813.

Fig.
1. A Three-compartment unified Gadoxetate DCE-MRI liver model. The light grey
box models liver tissue - either a voxel, ROI, segment or whole liver. The dark
grey boxes represent the compartments within liver tissue.

Table 1. Equations for models
1-4, derived from a unified gadoxetate DCE-MRI model, derived using the given
assumptions.

Fig. 2 (a-c) Means and standard deviations of $$$v_e, k_{he}$$$, and $$$k_{bh}$$$ on Days 1 and 2 and (d-f) % coefficients of variation
in $$$v_e, k_{he}$$$, and $$$k_{bh}$$$ on the two days, averaged over all rats, measured
using Models 1-4.