Determination of hepatic extraction fraction with gadoxetate low-temporal resolution DCE-MRI-based deconvolution analysis: validation with ALBI score and Child-Pugh class

Abstract

Introduction

In this study, we aimed to investigate the feasibility of gadoxetate low-temporal resolution (LTR) DCE-MRI for voxel-based hepatic extraction fraction (HEF) quantification for liver sparing radiotherapy using a deconvolution analysis (DA) method.

Methods

The accuracy and consistency of the deconvolution implementation in estimating liver function was first assessed using simulation data. Then, the method was applied to DCE-MRI data collected retrospectively from 64 patients (25 normal liver function and 39 cirrhotic patients) to generate HEF maps. The normal liver function patient data were used to measure the variability of liver function quantification. Next, a correlation between HEF and ALBI score (a new model for assessing the severity of liver dysfunction) was assessed using Pearson's correlation. Differences in HEF between Child-Pugh score classifications were assessed for significance using the Kruskal–Wallis test for all patient groups and Mann–Whitney U-test for inter-groups. A statistical significance was considered at a P-value <0.05 in all tests.

Results

The results showed that the implemented method accurately reproduced simulated liver function; root-mean-square error between estimated and simulated liver response functions was 0.003, and the coefficient-of-variance of HEF was <20%. HEF correlation with ALBI score was r = −0.517, P < 0.0001, and HEF was significantly decreased in the cirrhotic patients compared to normal patients (P < 0.0001). Also, HEF in Child-Pugh B/C was significantly lower than in Child-Pugh A (P = 0.024).

Conclusion

The study demonstrated the feasibility of gadoxetate LTR-DCE MRI for voxel-based liver function quantification using DA. HEF could distinguish between different grades of liver function impairment and could potentially be used for functional guidance in radiotherapy.

Introduction

Global Liver function is the most significant determinant for predicting treatment outcomes in liver cancer radiotherapy.¹ It is generally measured using clinical scoring systems, including Child-Pugh class/score (CPS), the model for end-stage liver disease (MELD) score, the ALBI (albumin-bilirubin) score, and indocyanine green retention rate at 15 min (ICG-R15).²

The ICG-R15 is typically calculated from liver clearance of ICG at 15 min after injection. It is recommended for assessment of global liver function in hepatocellular carcinoma (HCC) patients with underlying cirrhosis prior to liver resection.^3-5 The CPS is also widely used in routine clinical practice for prognosis due to the simplicity of score determination calculated from serum bilirubin, albumin, prothrombin time, hepatic encephalopathy and ascites. The specificity of the CPS in assessing prognosis in HCC patients was found to be higher than the MELD score which is determined by bilirubin, creatinine and international normalised ratio.⁶ The ALBI score is a new and objective measure of global liver function assessment in HCC patients with cirrhosis. This model combines serum albumin and bilirubin without requiring the presence of ascites and encephalopathy, which are more subjective determinants of liver failure.⁷ Previous studies reported that this model accurately predicted patient mortality in HCC and was better than both CPS and MELD scores.^7,8 A recent study reported that CPS, MELD and ALBI were reliable measures in predicting mortality for both short-term and long-term prognosis in cirrhotic patients.⁹

However, these current approaches remain limited in radiation therapy treatment planning as they do not provide spatial liver function, which limits the ability to spare higher functioning liver tissues from radiation dose. Therefore, image-based liver function quantification has been recently proposed to assess spatial liver function. Gadoxetate DCE-MRI in particular has shown growing interest due to its availability and the fact that MRI is an ionising radiation-free modality.

There are two main approaches for assessing spatial liver function using DCE-MRI, that is, deconvolution analysis (DA)^10-12 and pharmacokinetic tissue-compartment modelling.^13,14 Both methods allow estimation of both hepatic function and liver tissue perfusion. The pharmacokinetic modelling takes into account plasma flow, allowing estimation of hepatic uptake rate and perfusion rate separately. However, it requires a high-temporal resolution DCE-MRI, tissue compartment determination and the optimisation of unknown variables in the model.^14,15

In comparison, the deconvolution analysis method can be used to estimate the hepatic extraction fraction (HEF) of gadoxetic acid, a hepatocyte-specific contrast agent. It does not require definition of tissue compartments.¹⁶ The HEF parameter represents liver function efficacy in extracting gadoxetic acid from the first pass of blood plasma bolus after gadoxetate administration. It was initially introduced in hepatobiliary ^99mTc-IDA scintigraphy.^17,18 Previous studies have proposed the MRI-based HEF parameter for liver function quantification and showed that they could discriminate between healthy liver function volunteers and patients with hepatobiliary disease.^10-12 However, its use has been limited because imaging acquisition protocols have been long, although the method does not require a sophisticated mathematic model. A study by Yamada et al. proposed hepatocellular uptake index (HUI) derived from gadoxetate disodium-enhanced hepatobiliary phase MRI to determine a regional remnant-liver-function. This static image volume was obtained at 20 min after gadoxetate disodium administration. HUI value was determined by a simple mathematic equation, VL(L20/S20–1), from liver volume (VL) and mean signal intensity of whole liver (L20) and whole spleen (S20). They reported that the HUI parameter significantly correlated with the plasma disappearance rate of indocyanine green (ICG-PDR).¹⁹ However, this method did not consider the time-signal course of liver tissue over imaging time, which can represent a physiological function of liver tissue in uptaking gadoxetic acid over imaging time and voxel-based liver function.

In routine liver MRI scans, clinical gadoxetate DCE-MRI is obtained within a shorter imaging time of less than 30 min using low-temporal resolution (LTR). However, these data are normally discarded for liver function quantification as the undersampled data can result in uncertain kinetic parameter values when using the pharmacokinetic model.²⁰ If HEF can be determined from LTR-DCE MRI data using the deconvolution analysis, its clinical utility would be improved, particularly for functional guidance in radiotherapy. Thus, this study hypothesised that the deconvolution analysis could be acceptable for measuring HEF in LTR-DCE MRI.

As an initial step for developing a radiotherapy liver function sparing method, this study aimed to investigate the feasibility of voxel-based HEF quantification using gadoxetate LTR-DCE MRI. To this end, we assessed the consistency of the deconvolution analysis method using numerical simulation, the variability of the HEF results in-vivo, correlation between the derived HEF and ALBI scores, and finally statistical differences between HEF and clinical CPS.

Methods Patient data

The study was ethically and scientifically reviewed and approved by the Hunter New England Human Research Ethics Committee, NSW, Australia. This study retrospectively assessed the Calvary Mater Newcastle hospital's PACS (picture archiving and communication system) database to collect MRI data conducted in 2019–2021. The clinical datasets comprised 64 patients who met the inclusion criteria with 25 normal liver function patients and 39 HCC patients with underlying chronic liver disease. The inclusion criteria for normal liver function patients included receiving gadoxetate DCE-MRI, having a biochemical blood result, having no clinical history of chronic liver diseases or liver malignancy. For liver disease patients, a diagnosis of liver cirrhosis was required for inclusion. Exclusion criteria included not receiving gadoxetate DCE-MRI, no biochemical blood result, alcoholic liver cirrhosis and severe motion artefacts on MRI images. Patient characteristics are summarised in Table 1.

Table 1 Patient characteristics.

Variable	Normal liver function (n = 25)	Cirrhotic patients (n = 39)	Reference range	P-value
Gender (Female/Male)	20/5	5/34		<0.001
Age (range) years	49.20 (18–74)	63.26 (51–79)		<0.001
Clinical diagnosis
Hepatocellular Carcinoma (HCC)		38
Oligometastasis+HCC		1
Biochemical blood test: mean (min–max)
Creatinine (μmol/L)	70.80 ± 1.84	88.07 ± 48.75	40–100	0.029
Albumin (g/L)	39.60 ± 4.23	33.72 ± 10.01	30–44	<0.001
Bilirubin total (μmol/L)	10.00 ± 4.17	26.72 ± 35.71	< 20	<0.001
Sodium (mEq/L)	139.16 ± 1.84	136.69 ± 3.77	135–145	0.005
INR	0.99 ± 0.33	1.16 ± 0.22	2–4.5	<0.001
Liver enzyme test: mean (min-max)
Alkaline Phosphatase (ALP) (U/L)	67.96 ± 28.42	131.62 ± 79.37	30–110	<0.001
Alanine Aminotransferase (ALT) (U/L)	23.24 ± 9.94	53.51 ± 48.92	10–50	0.001
Aspartate Aminotransferase (AST) (U/L)	22.76 ± 6.64	86.69 ± 136.07	<40	<0.001
CP class (score)
A (5–6)		26
B (7–9)		11
C (10–15)		2
ALBI score (mean ± SD)	−2.73 ± 0.32	−1.93 ± 0.57

ALBI, Albumin-Bilirubin; INR, International Normalised Ratio; MELD, Model of End-Stage Liver disease; U/L, units per litter; μmol/L, Micromoles Per Litre. All variables were significant differences at P < 0.05.

Magnetic resonance imaging

The gadoxetate LTR-DCE MRI examinations were performed with a 3 Tesla MAGNETOM Skyra (Siemens Healthineers, Erlangen, Germany) with an 18-channel body matrix phased-array coil. A Dixon 3D-spoiling gradient recalled echo T1-weighted sequence was employed during breath-hold with the following imaging parameters: repetition time (TR)/echo time (TE) = 3.56 ms/1.23 (TE1) and 2.46 (TE2) ms, flip angle(FA) = 9°, slice thickness = 3 mm, field-of-view (FOV) = 350–380 mm², slice number = 72–80 slices, scan time = 13 s, matrix size = 380 × 270 mm², and voxel size = 1.25 × 1.25 × 3 mm³. All liver volumes were acquired in the transaxial plane except the second delayed phase acquired in the coronal plane (voxel size = 1.406 × 1.406 × 2.0 mm³), and this was then reformatted into a transaxial plane.

Each liver volume was acquired within a single breath-hold. First, a single non-contrast phase of the liver volume was acquired for baseline prior to contrast injection. Then, a region-of-interest (ROI) for automatic gadoxetate bolus tracking was placed over the region of the left ventricle of the cardiac chambers to automatically detect the arrival of the first bolus of tracer following injection. Then, gadoxetic acid disodium (Gd-EOB-DTPA) was injected with a dose of 0.1 mL/kg (0.25 mmoL/mL) in the cubital vein of the patient's right arm using a power injector (Medrad® MRXperion™ Injection System, USA). The infusion flow rate was 1 mL per second, followed by normal saline at the same flow rate. After that the arterial phase was then acquired automatically following the arrival of the first bolus detection. This was followed by the porto-venous phase, first delayed phase and second delayed phase. Finally, the hepatobiliary phase was acquired 15–20 min after injection, as graphically illustrated in Appendix S1.

Image post-processing and analysis

Image post-processing was performed using the 3D slicer software (http://www.slicer.org). First, noise filtering was performed on the DCE-MRI data using median filtering (neighbourhood size: 2, 2, 2). Then, image volumes of arterial, porto-venous, delayed and hepatobiliary phases (moving volumes) were co-registered to a reference volume (fixed volume), non-contrast enhanced T1WI, using a deformable registration method (Elastix toolbox and 3D slicer software) developed by Andras Lasso (Queen's University, PerkLab).^21,22 The generic preset of Elastix was defined before selecting the fixed volume and a moving volume. This preset can be used for all anatomical regions. The registration accuracy between the reference image volume and moving image volumes was evaluated using visual inspection. Next, liver volume segmentation was performed for all image volumes. After that the output image volumes were processed in Matlab software (MATLAB ver. R2018b) for further analysis.

The total blood perfusion of the liver parenchymal tissue is mainly derived from the portal vein (approximately 75% of the total liver blood flow). The remaining blood supply is derived from the hepatic artery. Therefore, this study measured image signals of the portal vein to generate a time-signal course as a vascular input function. To do this, a binary mask image of the main portal vein was created by manually drawing a single region-of-interest (ROI) on the hilar region (ROI size range, 45–90 mm²) using the portal venous phase image as an anatomical reference. Then, the mean image signal intensity of the portal vein was quantified by applying the binary mask to all image volumes to generate the time-intensity course of the portal vein signal or vascular input function $\mathrm{VIF}\left(t\right)$. For the liver parenchyma tissue, the image signal intensity of each voxel i,j was automatically extracted from all volumes to generate the time-intensity signal of liver tissue or liver response function ${\mathrm{LRF}}_{i,j}\left(t\right)$. This process was performed using in-house software running in Matlab. Then, both signal time curves of ${\mathrm{LRF}}_{i,j}\left(t\right)$ and $\mathrm{VIF}\left(t\right)$ were normalised using the following equation:[Image Omitted. See PDF]where ${\widehat{\mathrm{SI}}}_{i,j}\left(t\right)$ is the relative signal intensity (SI) at time $t$ of voxel $i,j,{\mathrm{SI}}_{i,j}\left(t_0\right)$ is SI of the non-contrast baseline image volume at the initial time $t_0$, and ${\mathrm{SI}}_{i,j}\left(t\right)$ is SI at a given time $t$.¹²

Subsequently, least-square fitting was applied to both normalised $\mathrm{VIF}\left(t\right)$ and ${\mathrm{LRF}}_{i,j}\left(t\right)$ using a shape-preserving piecewise cubic Hermite interpolating polynomial (pchip) method. Then, fitted values of the curves with 15-data point intervals over the imaging time length were extracted and used in the model for further analysis. This process aims to increase data points from the original six data points acquired from LTR-DCE MRI to generate a signal time course of higher temporal resolution. This is necessary for the deconvolution analysis method to obtain meaningful ${\mathrm{IRF}}_{i,j}\left(t\right)$ results from the mathematical deconvolution method.

Truncated singular value decomposition-based deconvolution analysis

Previous studies have described the use of truncated singular value decomposition (TSVD) as an effective deconvolution analysis technique for measuring the proportion of tracer taken up by the hepatocytes.^10,12,23 In this study, we utilised the existing method proposed by Nilsson and colleagues¹² with a modification to be applicable to clinical DCE-MRI datasets, acquired in breath-hold with a low sampling rate.

Based on deconvolution analysis method, the response function of the liver tissue is mathematically determined from the convolution between the impulse response function and vascular input function:[Image Omitted. See PDF]where ${\mathrm{LRF}}_{i,j}\left(t\right)$ is the measured total liver response function, $\mathrm{VIF}\left(t\right)$ is the vascular input function from the portal vein, and ${\mathrm{IRF}}_{i,j}\left(t\right)$ is the unknown impulse response function and both $\tau$ and t are time variables.

The ${\mathrm{IRF}}_{i,j}\left(t\right)$ curve represents the first-pass analysis of a single bolus of MRI contrast agent instantaneously delivered into the liver and assuming that there was no subsequent recirculation over the imaging time. Therefore, in an idealised situation where gadoxetic acid was injected directly through the main portal vein without recirculation, ${\mathrm{LRF}}_{i,j}\left(t\right)$ would equal ${\mathrm{IRF}}_{i,j}\left(t\right)$, which would allow the determination of liver function from the ${\mathrm{LRF}}_{i,j}\left(t\right)$ curve directly. However, in routine practice $\mathrm{VIF}\left(t\right)$ is usually dispersed over the imaging time due to blood recirculation. Therefore, the unknown ${\mathrm{IRF}}_{i,j}\left(t\right)$ requires estimation using methods such as TSVD to account for the dispersion problem from blood recirculation.

To estimate ${\mathrm{IRF}}_{i,j}\left(t\right),$ deconvolution analysis of $\mathrm{VIF}\left(t\right)$ and ${\mathrm{LRF}}_{i,j}\left(t\right)$ was performed using the TSVD-based deconvolution method described in Appendix S1. Once the estimated ${\mathrm{IRF}}_{i,j}\left(t\right)$ was obtained, mono-exponential curve fitting was applied over a defined time period of ${\mathrm{IRF}}_{i,j}\left(t\right)$, with the fitted curve referred to as the hepatic retention curve ${\mathrm{HRC}}_{i,j}\left(t\right)$. The hepatic retention time was shorted to 900 s as compared to from 1800 s in the Nilsson method. The ${\mathrm{HRC}}_{i,j}\left(t\right)$ was then extrapolated to the initial time point (y-intercept value) to calculate the HEF at a voxel level denoted as ${\mathrm{HEF}}_{i,j}$ (Fig. 1) using the following equation.¹²[Image Omitted. See PDF]where $Y-\text{intercept of}{\mathrm{HRC}}_{i,j}\left(t\right)$ is the initial time point of the mono-exponential curve fitting after extrapolation. $\mathrm{Max}\left({\mathrm{IRF}}_{i,j}\left(t\right)\right)$ represents the vascular peak of liver tissue.

Figure 1. pchip-Curve fittings of LRF (dash-line) and VIF (bold-line) (A). The estimated IRF consists of the vascular phase, transition phase (120 s–300 s) and hepatic retention curve (HRC) defined from 420 s to 900 s (B).

The HEF parametric map was generated with values ranging from 0 to 1. However, image registration imperfections can cause artefacts at a voxel level; in particular, voxels in the outer region of the segmented liver volume can cause parametric map scaling errors. Based on the findings of previous studies and methodological considerations,^11,12,24 the high HEF values in the tail of the HEF histogram frequently correspond to artefacts. Thus, a histogram thresholding method was performed to select the optimal threshold level to remove artefacts visually. In this study, voxel values of ${\mathrm{HEF}}_{i,j}$ > 0.7 were regarded as artefacts and excluded from the analysis.

Consistency of deconvolution method using numerical simulation

Firstly, this study verified the mathematical implementation by simulations using pre-defined $\mathrm{VIF}\left(t\right)$ and $\mathrm{LRF}\left(t\right)$ functions as input to the model to verify that the model estimates the IRF correctly using equation (1). The derived $\mathrm{IRF}\left(t\right)$ was convolved with the predefined $\mathrm{VIF}\left(t\right)$ to generate $\mathrm{LRF}\left(t\right)$ which was compared to the predefined curve. Root-mean-square error was computed to determine the accuracy of the developed mathematic model.

Secondly, deconvolution is well known to suffer from noise magnification during data analysis. Therefore, the consistency of the method to calculate HEF values was assessed by simulating 1000 patterns with randomly generated additive Gaussian-noise distributions and hence varying signal-to-noise (SNR) levels. The SNRs comprised 14 levels, ranging from 5 to 70 in steps of 5. Then, the shape of the pre-defined $\mathrm{VIF}\left(t\right)$ and $\mathrm{LRF}\left(t\right)$ curves was altered to different SNRs by addition of the random-noise. Next, the HEF value was automatically calculated from the estimated $\mathrm{IRF}\left(t\right)$ with corresponding SNR. This process was repeated 1000 times for varying SNR. Finally, the average HEF and its consistency as specified by the coefficient-of-variation (CV) were computed for each SNR. CV was calculated from the SD and mean value division, [SD/mean] × 100%. The % CV is considered very good when CV < 10%, good when 10% ≤ CV < 20%, acceptable when 20% ≤ CV ≥30%, and unacceptable when CV > 30%.²⁵

Variability of measurements (in-vivo)

The DCE-MRI data of 25 normal liver function patients were used to investigate inter-subject variability by comparing results for both ROI-based and voxel-based methods.

ROI-based liver function quantification was performed by manually drawing a single ROI (area average, 1201.4 ± 545.3 mm²) over each liver segment (Segment I–VIII) using one slice above and one slice below the mid-level of the liver and using the main portal vein as an anatomical landmark. Care was taken to avoid hepatic vessels and artefacts. Subsequently, the average signal of all voxels in the ROI was used to derive an ${\mathrm{LRF}}_k\left(t\right)$ for each liver segment k, while the $\mathrm{VIF}\left(t\right)$ was derived from the portal vein. Finally, ${\mathrm{HEF}}_k$ was calculated for all liver segments separately and then averaged. Subsequently, the mean value and SD across liver segments were used to compute the CV (%).

For the voxel-based method, the ${\mathrm{HEF}}_{i,j}$ voxels were averaged over the whole liver volume of the HEF map. The CV was then computed from the average value and standard deviation across voxels within the liver volume.

Assessing correlation between HEF and ALBI score

Bilirubin and albumin data collected from biochemical blood results on the same day as the MRI scans were used to calculate ALBI scores using the following formula, ALBI score = (log₁₀ bilirubin × 0.66) (albumin × 0.085), where bilirubin is in μmol L⁻¹ and albumin in g L⁻¹. Then, a linear correlation between average HEF and ALBI score was assessed as a part of LTR-DCE-MRI-derived HEF validation.

Comparison of MRI-derived HEF across patient groups

Three groups of patients, including normal liver function, CPS A, and CPS B/C, were statistically compared to median global HEF values both across the groups and between groups.

Statistical analysis

The HEF values were expressed as mean, median, range and standard deviation (SD) using SPSS24 (SPSS, Chicago, IL, USA). A Pearson correlation coefficient was utilised to assess correlation between the continuous variables HEF and ALBI scores. Furthermore, Mann–Whitney's U-test was employed to assess the statistical differences between HEF results and CPS categories, and significant differences across all categories were investigated using the Kruskal–Wallis test. All tests were considered statistically significant at P < 0.05.

Results The consistency of the DA method using numerical simulation

The RMSE between the estimated $\mathrm{LRF}$(t) and measured $\mathrm{LRF}$(t) was 0.003, confirming that the developed DA method correctly estimated $\mathrm{IRF}$(t). Figure 2 illustrates that the variability of HEF values increased with the decreased SNR. The SNR25 was the lowest SNR level, where the model could tolerate noise (CV = 17.7%) in the numerical testing, and the HEF variability at SNR70 was 0.07%.

Figure 2. The percentage of coefficient of variation (CV) of hepatic extraction fraction values, calculated from different SNR levels with random noise distributions. The CV increased with decreasing SNR.

Variability of measurements (in vivo)

Table 2 shows that the inter-subject variability (CV) of HEF quantified by the ROI-based method was 19.3% which was similar to the voxel-based method, which was 19.2%. This was considered acceptable variability for both methods.

Table 2 Comparing global HEF quantification using different methods in 25 normal liver function patients.

Variable	ROI-based method	Voxel-based method
Mean	0.309	0.312
Median	0.308	0.311
Min	0.187	0.189
Max	0.416	0.420
SD	0.060	0.060
CVinter	19.3%	19.2%

CV_inter, inter-subject variability; HEF, hepatic extraction fraction.

Correlation between HEF and ALBI score

Figure 3A shows a negative correlation of HEF with ALBI score (r = −0.517; 95% CI: −0.674, −0.327; P = 0.000). HEF tended to decrease with increasing ALBI scores and increased severity of liver function impairment.

Figure 3. (A) Significant linear correlation between hepatic extraction fraction (HEF) and ALBI score as the reference liver function measure using Pearson's correlation. (B) Statistically significant difference of mean HEF calculated from all voxels within the liver volume across different grades of liver dysfunction. HEF was significantly decreased in patients assessed using Kruskal–Wallis for all groups and Mann–Whitney U-tests for inter-group. *P [less than] 0.01, **P [less than] 0.05.

Comparison of MRI-derived HEF across patient groups

The median HEF (min–max) values of normal liver function, CPS A and CPS B/C groups were 0.32 (0.19–0.42), 0.12 (0.04–0.29) and 0.08 (0.02–0.15), respectively. The median HEF significantly decreased in cirrhotic patient groups (P < 0.0001). In addition, the HEF of the CPS B/C group was significantly lower than CPS A (P = 0.024), as shown in Figure 3B.

Figure 4 shows the comparison of gadoxetate-enhanced hepatobiliary phase images (upper row) and LTR-DCE MRI-derived HEF maps (lower row). The hepatobiliary phase image and HEF map of normal liver function patient are shown in the first column (A, D), mild liver function impairment patient (CP-A) in the middle column (B, E) and moderate liver function impairment patient (CP-B7) in the third column (C, F). The signal intensity of the gadoxetate-enhanced hepatobiliary phase image and the HEF map of the normal liver function patient seem more homogenous than cirrhotic patients (CP-A and CP-B).

Figure 4. Comparison of hepatobiliary phase images and the hepatic extraction fraction (HEF) maps of a normal liver function patient (A/D), diagnosed cirrhotic patient with Child-Pugh (CP)-A5 disease (B/E), and a cirrhotic patient with CP-B7 (C/F), which visually increases HEF's heterogeneity spatially.

Discussion

In this study, we successfully applied a deconvolution-based method for liver function extraction and quantification using six-phase LTR-DCE MRI with a modification to an existing method developed for higher temporal resolution data. We assessed the implemented method's accuracy with simulation studies by comparing the estimated $\mathrm{LRF}\left(t\right)$ with predefined $\mathrm{LRF}\left(t\right)$ after convolving the known input functions (measured $\mathrm{VIF}\left(t\right)$ and estimated $\mathrm{IRF}\left(t\right)$). We found that the RMSE, frequently used to measure the differences between model predicted values and measured values, was closed to zero. This means that the model estimated $\mathrm{LRF}\left(t\right)$ correctly as the predefined $\mathrm{LRF}\left(t\right)$ and estimated $\mathrm{LRF}\left(t\right)$ closely resemble each other. Also, HEF was consistently calculated with varying SNR of the input data using the implemented method as the results showed a low variation of HEF value (0.07%) for SNR 70.

For in vivo testing, the inter-patient variability of HEF in normal liver function patients was measured and compared using both region-based (average signal in region) and voxel-based methods. The results showed that the method yielded comparable region-based and voxel-based HEF quantifications with acceptable variability (CV < 20%) for both methods. When assessing HEF values in patient groups, the derived HEF parameter could differentiate between normal liver function and liver dysfunction patients.

Although different DCE-MRI data types were used, the results of this study corresponded to Nilsson et al.¹¹ HEF of the patient group was significantly decreased compared with the normal group. The decrease of HEF in liver dysfunction patients corresponds to the degree of severity of liver dysfunction, resulting in altered gadoxetate uptake and retention in the liver.²⁶ In addition to Nilsson's study, this current study has validated the derived parameters with ALBI scores, a new approach for global liver function quantification in HCC patients with underlying cirrhosis. HEF was correlated with ALBI scores; the decreased HEF corresponded to decreased liver function, represented by an increased ALBI score. Thus, this study has shown that deconvolution analysis was an acceptable method for evaluating hepatocellular function efficacy using LTR-DCE MRI datasets.

In this study, the DA method was modified from the study of Nilsson and colleagues to enable its use with the clinical data of LTR-DCE MRI. The study has shortened the hepatic retention curve range from 7–30 min to 7–15 min after gadoxetic acid administration as the LTR-DCE MRI generally lasts 15–20 min after injection. The shortened HRC can resolve the overlap between the hepatic retention phase and excretion phase of gadoxetate to the bile. Also, the starting time of HRC at 7 min after injection^12,23 can avoid overlapping of the transitional phase, typically occurring within ~2–5 min after injection, and the initial hepatic retention phase.²⁷ The overlapping of tracer uptake, transit and excretion can cause difficulty in actual HEF estimation.²⁸ Furthermore, the power curve fitting (power 1) was utilised to remove the staircasing effect of the estimated IRF, normally found in the standard TSVD.

Previous studies also proposed using clinical LTR-DCE MRI data in assessing liver function. For example, Yamada et al. utilised the static image of gadoxetate-enhanced MRI to derive HUI parameter, an image intensity-based parameter. They found that HUI correlated with the ICG clearance test, a standard measure of global liver function (0.721; 95% CI:0.717–0.726).¹⁹ However, this method was a region-based liver function method that could be limited in functional avoidance radiation treatment planning requiring voxel-based liver function information. Compared to Yamada et al.'s method, the HEF map derived from our method could determine liver function at a voxel level, allowing a function-based radiation treatment plan for sparing. The radiation dose for treatment can be precisely given to the target at a voxel level; therefore, it is reasonable to provide liver function at this level.

In addition, Saito et al. deployed a five-phase LTR-DCE MRI to derive uptake rate (UR) and the distribution of extravascular extracellular volume (Ve) parameters for liver function quantification. They validated UR and Ve with the CPS class as a standard liver function measure. They found that only the UR parameter could distinguish between non-cirrhosis and CPS A and B cirrhosis.²⁹ However, the variability of the UR parameter still requires investigation. The result of their study corresponds to this current study, showing a significant difference in global HEF values across patient groups.

Some limitations arose during the study. First, this study was a retrospective study using non-ideal data for analysis. The inconsistency of data-sampling rates (frame per second) and gap times between volumes could result in variation of the quantitative values. This study utilised multiphasic liver volumes of LTR-DCE MRI. The original data were sampled with 15 s acquisition time per volume over the imaging time, resulting in varying HEF values. Therefore, we solved this problem by applying curve fitting to generate synthetic high-temporal resolution data in this study. However, the method could still be underestimating the peak enhancement and hence underestimating the HEF.

Second, although the ICG clearance test is an effective method in evaluating cirrhotic severity in HCC patients, this study was unable to validate HEF with this metric due to our patient dataset not having this information.³⁰ However, CPS class/score and ALBI score are reliable methods to predict both long-term and short-term prognosis in cirrhotic patients.⁹ Validating HEF derived from LTR-DCE MRI with ICG clearance test could improve the significance of this parameter in further study.

Third, this study did not deploy the dual-inlet tissue compartment model for liver function assessment, although this model could overcome the limitations of the DA method in measuring arterial blood flow, porto-venous blood flow of liver tissue and hepatic function separately within a single acquisition.¹⁴ This is because LTR-DCE MRI data could, in turn, influence the reliability of the kinetic parameters of both liver perfusion and function. However, the DA method should be acceptable for liver function estimation using LTR-DCE MRI. This study suggested that a novel high-temporal resolution DCE-MRI pulse sequence, allowing multiple image volume acquisitions within a single breath-hold, could help to improve this limitation in a further prospective study.

Lastly, the study only compared the results with two classes of liver dysfunction (CP-A and B/C) as the number of CP-C patients was relatively low. In addition, this study was only conducted in a single centre with a limited number of patients. Further research is warranted to determine the applicability of this technique in a prospective multi-institutional study or a larger sample size.

Conclusion

This study investigated the feasibility of utilising gadoxetate LTR-DCE MRI in assessing spatial liver function using deconvolution analysis. Also, the results indicated the potential use of MRI-derived HEF parameter as imaging biomarkers for liver function quantification, showing correlation with ALBI score and statistically significant differences of HEF between normal liver function patients and different CPS categories. Therefore, the HEF map could be feasible in determining sparing functional regions in radiation therapy for future investigation.

Acknowledgements

We would like to express our gratitude to the following individuals, who are a former member of the Medical Physics Research Group at Calvary Mater Newcastle, for their expertise and assistance: Dr. Danny Lee (Radiation Oncology, Allegheny Health Network, USA) and Jose Baozi Ortega. Monchai Phonlakrai gratefully acknowledges the funding received towards his PhD from the Chulabhorn Royal Academy, Thailand.

Conflict of Interest

The authors declare no conflict of interest.