Gadoxetate-enhanced MR imaging and compartmental modelling to assess hepatocyte bidirectional transport function in rats with advanced liver fibrosis

Abstract

Objectives

Changes in the expression of hepatocyte membrane transporters in advanced fibrosis decrease the hepatic transport function of organic anions. The aim of our study was to assess if these changes can be evaluated with pharmacokinetic analysis of the hepatobiliary transport of the MR contrast agent gadoxetate.

Methods

Dynamic gadoxetate-enhanced MRI was performed in 17 rats with advanced fibrosis and 8 normal rats. After deconvolution, hepatocyte three-compartmental analysis was performed to calculate the hepatocyte influx, biliary efflux and sinusoidal backflux rates. The expression of Oatp1a1, Mrp2 and Mrp3 organic anion membrane transporters was assessed with reverse transcription polymerase chain reaction.

Results

In the rats with advanced fibrosis, the influx and efflux rates of gadoxetate decreased and the backflux rate increased significantly (p = 0.003, 0.041 and 0.010, respectively). Significant correlations were found between influx and Oatp1a1 expression (r = 0.78, p < 0.001), biliary efflux and Mrp2 (r = 0.50, p = 0.016) and sinusoidal backflux and Mrp3 (r = 0.61, p = 0.002).

Conclusion

These results show that changes in the bidirectional organic anion hepatocyte transport function in rats with advanced liver fibrosis can be assessed with compartmental analysis of gadoxetate-enhanced MRI.

Key Points

• Expression of hepatocyte transporters is modified in rats with advanced liver fibrosis.

• Kinetic parameters at gadoxetate-enhanced MRI are correlated with hepatocyte transporter expression.

• Hepatocyte transport function can be assessed with compartmental analysis of gadoxetate-enhanced MRI.

• Compartmental analysis of gadoxetate-enhanced MRI might provide biomarkers in advanced liver fibrosis.

Appendix

By assuming linear tracer kinetics to describe uptake and elimination of gadoxetate in hepatocytes [12], kinetic indexes can be derived by the linear system theory such as:

$$ \frac{{\mathrm{dx}}^{\mathrm{j}}\left(\mathrm{t}\right)}{\mathrm{dt}}={\mathrm{A}}_{\mathrm{j}\mathrm{i}}{\mathrm{x}}^{\mathrm{i}}\left(\mathrm{t}\right)+{\mathrm{B}}_{\mathrm{j}\mathrm{i}}{\mathrm{u}}^{\mathrm{i}}\left(\mathrm{t}\right) $$

(1.1)

The xⁱ(t), j, i = 1…n with n the number of compartments, describe the time t evolution of gadoxetate in each compartment. A_ji is the flow into and out of each compartment, uⁱ(t) are the input control functions for each compartment and B_ji the matrix describing the method of control application. By integrating Eq. 1.3 with xⁱ(0) = 0 for all i as initial conditions:

$$ {\mathrm{x}}^{\mathrm{j}}\left(\mathrm{t}\right) = {\mathrm{e}}^{\mathrm{Aji}\mathrm{t}}{\mathrm{x}}^{\mathrm{i}}(0)+{\displaystyle \underset{0}{\overset{\mathrm{t}}{\int }}}{\mathrm{d}\uptau \mathrm{e}}^{\mathrm{Aji}\left(\mathrm{t}-\uptau \right)}{\mathrm{B}}_{\mathrm{j}\mathrm{i}}{\mathrm{u}}^{\mathrm{i}}\left(\uptau \right) $$

(1.2)

Here, h(t) can be decomposed as the sum of the evolution of the gadotexate concentration into two compartments (hepatocytes and intra-hepatic bile ducts):

$$ h(t)={x}^1(t)+{x}^2(t) $$

(1.3)

$$ \mathrm{h}\left(\mathrm{t}\right)={\mathrm{k}}_{21}{\displaystyle \underset{0}{\overset{\mathrm{t}}{\int }}}\mathrm{d}\uptau \left[{\mathrm{e}}^{-\left({\mathrm{k}}_{32}+{\mathrm{k}}_{12}\right)\mathrm{t}}\left(\mathrm{t}-\uptau \right)+\left(\frac{{\mathrm{k}}_{32}}{{\mathrm{k}}_{32}+{\mathrm{k}}_{12}-{\mathrm{k}}_3}\left({\mathrm{e}}^{-{\mathrm{k}}_3\mathrm{t}}-{\mathrm{e}}^{-\left({\mathrm{k}}_{32}+{\mathrm{k}}_{12}\right)\mathrm{t}}\right)\right)\left(\mathrm{t}-\uptau \right)\right]\mathrm{B}\left(\uptau \right) $$

(1.4)

$$ \mathrm{h}\left(\mathrm{t}\right)={\mathrm{k}}_{21}{\displaystyle \underset{0}{\overset{\mathrm{t}}{\int }}}\mathrm{d}\uptau \left[{\mathrm{e}}^{-\left({\mathrm{k}}_{32}+{\mathrm{k}}_{12}\right)\mathrm{t}}\left(\mathrm{t}-\uptau \right)+\left(\frac{{\mathrm{k}}_{32}}{{\mathrm{k}}_{32}+{\mathrm{k}}_{12}-{\mathrm{k}}_3}\left({\mathrm{e}}^{-{\mathrm{k}}_3\mathrm{t}}-{\mathrm{e}}^{-\left({\mathrm{k}}_{32}+{\mathrm{k}}_{12}\right)\mathrm{t}}\right)\right)\left(\mathrm{t}-\uptau \right)\right] $$

(1.5)

$$ \mathrm{h}\left(\mathrm{t}\right) = {\mathrm{k}}_{21}-\frac{{\mathrm{k}}_{21}{\mathrm{k}}_{32}}{{\mathrm{k}}_{32}+{\mathrm{k}}_{12}-{\mathrm{k}}_3}{\mathrm{e}}^{-\left({\mathrm{k}}_{32}+{\mathrm{k}}_{12}\right)\mathrm{t}}+\frac{{\mathrm{k}}_{21}{\mathrm{k}}_{32}}{{\mathrm{k}}_{32}+{\mathrm{k}}_{12}-{\mathrm{k}}_3}{\mathrm{e}}^{-{\mathrm{k}}_3\mathrm{t}} $$

(1.6)