Dual-input two-compartment pharmacokinetic model of dynamic contrast-enhanced magnetic resonance imaging in hepatocellular carcinoma

Table 1 Inclusion and exclusion criteria of the enrolled patients

Eligibility criteria	Exclusion criteria
Histopathology confirmed	MRI examination contraindication
Non-invasive diagnosis criteria [(EASL) 2012]1	Significant renal insufficiency
Cirrhotic patients
Hypervascular in the arterial phase
Washout in the portal venous or delayed phase
Non-antineoplaston therapy	Severe motion artifacts on MRI images
The largest diameter of lesion ≥ 2 cm	Hepatic vein/portal cancer embolus
Age of patients ≥ 18 yr	Inferior vena cava embolus
	Inability of informed written consent

¹European Association for the Study of the Liver suggested non-invasive diagnosis criteria on 4-phase multidetector CT scan[13]. EASL: European Association for the Study of the Liver; MRI: Magnetic resonance imaging.

Table 2 Summary of parameter terms used in the dual-input extended Tofts model and 2-compartment exchange model

Symbol	Definition	Unit
Ctiss(t)	Concentration of tracer in the tissue	mmol/L
CA(t)	Concentration of tracer in whole blood in a major feeding artery	mmol/L
Cv(t)	Concentration of tracer in the portal vein	mmol/L
Fa	Arterial fraction of the tissue perfusion	%
HLV	Hematocrit in major (large) vessels	none
HPI	Hepatic perfusion index	none
Fp	Flow rate of the blood plasma through the intravascular plasma space	mL/mL per minute
vp	Ratio of blood plasma volume to tissue volume	%
ve	Ratio of EES volume to tissue volume	%
kep	Efflux rate constant	min-1
Ktrans	Transfer constant	min-1
PS	Endothelial permeability surface area product	mL/mL per minute
⊗	Convolution operator	None

EES: Extravascular extracellular space.

Table 3 Patients’ demographic characteristics, tumor volume, and tumor stage

Age (yr)	Gender	Diagnosis criteria	Size (cm³)	Stage (BCLC)1
64.857 ± 10.384	Female 5	Confirmed by histology 8	409.588	A2 (2)
	Male 23	Diagnosed by EASL 20		A3 (3)
				A4 (1)
				B (11)
				C (11)

¹Barcelona-Clínic Liver Cancer classification[13]. EASL: European Association for the Study of the Liver.

Table 4 Comparison of tumor dynamic contrast-enhanced-magnetic resonance imaging pharmacokinetic parameters from 28 scanned patients using two models [Median (IQR)]

	ktrans (min-1)	PS (mL/mL ・min-1)	Fp (mL/mL ・min-1)	kep (min-1)	ve	vp	HPI
Dual-Input Extended Tofts model	0.29 ± 0.38	-	-	1.35 ± 1.42	0.51 ± 1.16	0.12 ± 0.21	0.66 ± 0.24
Dual-Input Exchange model	-	0.19 ± 0.36	1.07 ± 1.73	0.95 ± 1.60	1.22 ± 1.19	0.14 ± 0.17	0.63 ± 0.29
Z/t value	NA	NA	NA	-0.638	-2.869	-0.568	0.4991
P value	NA	NA	NA	0.524	0.004	0.569	0.6221

¹Paired t-test. NA: Not available; HPI: Hepatic perfusion index.