Satyam Ghodasara^{1}, Vikas Gulani^{2}, and Yong Chen^{2}

^{1}Case Western Reserve University School of Medicine, Cleveland, OH, United States, ^{2}Radiology, Case Western Reserve University, Cleveland, OH, United States

### Synopsis

**The dual-input
two-compartment model was applied to liver perfusion data, and significant
differences in perfusion parameters were found between normal hepatic
parenchyma and focal lesions, and also between HCC and metastatic lesions. These
findings support the possibility of using a two-compartment model with 3D free-breathing
acquisitions, for lesion characterization.**### Purpose

Quantitative liver perfusion imaging using DCE-MRI has been recently developed to investigate various liver pathologies

^{1}. While recent studies with a dual-input single-compartment model have shown significant differences in perfusion parameters between different types of focal lesions

^{2,3}, it has been suggested that a more appropriate kinetics model for certain pathological settings such as neoplasms utilizes two tissue compartments

^{4}. This model accounts for the heterogeneity of pathological tissue (which is not composed of just sinusoids), as well as the hepatic artery and portal vein inputs. Thus far, this model has been applied with repeated breath-holds interrupted to allow the patient to breathe. The objective of this study is to test the feasibility of applying this model to 3D free-breathing liver DCE data in the setting of hepatocellular carcinoma (HCC) and metastatic disease, acquired using 3D Through Time Spiral GRAPPA acceleration.

### Methods

The dual-input two-compartment model has been developed and described in depth by Koh, et al^{4}. Key details of the model are given here to familiarize the reader with the model. The contrast agent concentration-time curves in the liver tissue, hepatic artery, and portal vein are represented by *C*_{t}(t), *C*_{a}(t), and *C*_{p}(t), respectively. Blood flow from the hepatic artery and portal vein are represented by *F*_{a} and *F*_{p}, respectively. *F* represents the total blood flow to the liver and is equal to the sum of *F*_{a} and *F*_{p}. $$$ \alpha $$$ is the arterial fraction of the total blood flow to the liver and is equal to *F*_{a}/F. All of these quantities are related in the following formula: $$ C_t(t) = \left[ F_aC_a(t) + F_p C_p(t) \right] \ast R(t) = F\left[ \alpha C_a(t) + (1-\alpha)C_p(t) \right] \ast R(t) $$where $$$ * $$$ represents the convolution of the two functions. *R(t)* is the tissue impulse residue function and is the sum of two functions, *R*_{1}(t) and *R*_{2}(t), which are represented as$$ R_1(t) = u(t) - u(t-t_1) $$and$$ R_2(t) = u(t) \left\{ 1 - \exp \left(-\frac{PS}{F}\right) \times \left[ 1 + \int_0^t \exp\left(-\frac{PS}{v_2}\tau \right) \sqrt{\frac{PS}{v_2} \frac{PS}{F} \frac{1}{\tau}} I_1 \left(2 \sqrt{\frac{PS}{v_2} \frac{PS}{F}\tau}\right)d \tau\right] \right\}$$*u(t)* represents the Heaviside unit step function. *t*_{1} represents the mean time for blood to flow through the vasculature. *v*_{2} is the fractional volume of the pathological tissue compartment, *PS* is the permeability-surface area product of the pathological tissue vasculature, and *I*_{1} is the modified Bessel function. The dual-input two-compartment model was applied to 3D liver perfusion imaging data acquired from a Siemens 3T Skyra scanner. 7 normal volunteers (M:F, 4:3; mean age 20.8 years) and 11 patients (M:F, 9:2; mean age 64.3 years; 6 with metastatic adenocarcinoma with 39 total lesions, 5 with HCC with 13 total lesions) were included in this study. For each subject, high spatiotemporal resolution 3D whole-liver images (1.9×1.9×3.0 mm3; 60 partitions; 1.6 ~ 2 seconds acquisition time) were acquired using the through-time spiral GRAPPA technique with an in-plane reduction factor of 6. A total of 100 to 120 volumes for each subject were acquired continuously in about 4 min, while the subjects were breathing freely.

### Results and Discussion

Fig. 1 shows
representative liver perfusion maps obtained from a normal subject and Fig. 2
shows the perfusion maps from a patient with multiple metastatic lesions. A
summary of all the perfusion parameters obtained from the 7 normal subjects and
13 patients is presented in Table 1. Compared to results from the normal
volunteers, significant differences were observed in

*F*, $$$ \alpha $$$,

*v*_{2},

*PS* and

*t*_{1} for patients with metastatic adenocarcinoma (P<0.005), and in

*F*, $$$ \alpha $$$,

*PS* and

*t*_{1} for patients with HCC (P<0.05). A statistical
difference was also observed in

*F* and

*v*_{2} between metastases and HCC (P<0.005, Table 1).

### Conclusion

The dual-input
two-compartment model was successfully applied to 3D free-breathing
liver perfusion data acquired from both
normal subjects and patients with different focal lesions. Significant differences
in perfusion parameters were found between normal hepatic parenchyma and focal
lesions, and also between different types of lesions. As expected, arterial
fraction in both lesion types is higher than in normal parenchyma. Total
perfusion,

*F*, is found to be higher
in lesions, and is higher in metastatic lesions than in HCC. Fractional
volume of the pathological tissue compartment is higher in adenocarcinoma
metastases than HCC. We continue to explore the physiological implications of these
findings. Further investigation is needed to explore whether a two-compartment
model offers advantages in quantitative lesion characterization over a single
compartment model. More data will be needed for direct comparison of these
techniques. This study demonstrates initial feasibility of utilizing a
two-compartment model in 3D free-breathing lesion characterization.

### Acknowledgements

Siemens Healthcare and NIH grants 1R01DK098503,
R00EB011527, 1R01HL094557, and 2KL2TR000440.### References

1. Chen Y, et al. Invest
Radiol, 2015;50:367-375. 2. Bultman EM, et al. JMRI, 2014;39:853-865. 3. Chen
Y, et al. Int. Soc. Magn. Reson. Med. 2015;p386. 4. Koh TS, et al. MRM,
2011;65:250-260.