Kinetic 18F-FDG PET/CT imaging of hepatocellular carcinoma: a dual input four-compartment model

Background The endoplasmic reticulum plays an important role in glucose metabolism and has not been explored in the kinetic estimation of hepatocellular carcinoma (HCC) via 18F-fluoro-2-deoxy-d-glucose PET/CT. Methods A dual-input four-compartment (4C) model, regarding endoplasmic reticulum was preliminarily used for kinetic estimation to differentiate 28 tumours from background liver tissue from 24 patients with HCC. Moreover, parameter images of the 4C model were generated from one patient with negative findings on conventional metabolic PET/CT. Results Compared to the dual-input three-compartment (3C) model, the 4C model has better fitting quality, a close transport rate constant (K1) and a dephosphorylation rate constant (k6/k4), and a different removal rate constant (k2) and phosphorylation rate constant (k3) in HCC and background liver tissue. The K1, k2, k3, and hepatic arterial perfusion index (HPI) from the 4C model and k3, HPI, and volume fraction of blood (Vb) from the 3C model were significantly different between HCC and background liver tissues (all P < 0.05). Meanwhile, the 4C model yielded additional kinetic parameters for differentiating HCC. The diagnostic performance of the top ten genes from the most to least common was HPI(4C), Vb(3C), HPI(3C), SUVmax, k5(4C), k3(3C), k2(4C), v(4C), K1(4C) and Vb(4C). Moreover, a patient who showed negative findings on conventional metabolic PET/CT had positive parameter images in the 4C model. Conclusions The 4C model with the endoplasmic reticulum performed better than the 3C model and produced additional useful parameters in kinetic estimation for differentiating HCC from background liver tissue. Supplementary Information The online version contains supplementary material available at 10.1186/s40658-024-00619-1.


Introduction
Primary liver cancer was the sixth most commonly diagnosed cancer and the third leading cause of cancer death worldwide in 2020, with hepatocellular carcinoma (HCC) accounting for 75-85% of cases [1].
18F-fluoro-2-deoxy-d-glucose ( 18 F-FDG) positron emission tomography (PET)/computed tomography (CT) is a noninvasive imaging method for the diagnosis and evaluation of HCC that provides functional and molecular information [2,3].Dynamic PET/ CT imaging enables accurate quantification of radiotracer inflow and uptake via kinetic analysis of 18 F-FDG accumulation [4][5][6][7].Continuous exploration has driven PET kinetics research, the advent of total-body PET has improved photon capture capabilities, and fast dynamic imaging with high temporal resolution has become feasible [5,8,9].Moreover, more efficient algorithms are used to improve the accuracy of kinetic parameter estimation [10,11].
A hypothetical kinetic model is critical and is proposed based on the biological process of drugs in cells to obtain kinetic parameters for the evaluation of physiological and pathological conditions to help cancer screening, diagnosis and treatment [12].The two-compartment model merely describes tracer transport from blood to tissue, without further metabolic steps, and is appropriate only for transport markers.The threecompartment model describes the transport of markers between blood and tissue and the specific metabolic or binding target of radioactive markers [13,14].Wang et al. [15] proposed an optimized three-compartment model for the liver that adopted the optimally derived dual blood input function and the image-derived aortic input function and considered the dephosphorylation (k 4 ) and fractional blood volume (V b ) of 18 F-FDG.The six parameters of the three-compartment model are generally accepted and consistent with those of liver 18 F-FDG kinetic analysis [16][17][18][19].
The endoplasmic reticulum (ER) is the preferential site of 18 F-FDG accumulation, and phosphorylated 18 F-FDG enters the ER via the transmembrane protein glucose-6-phosphate transporter protein (G6PT), where it is hydrolysed to produce free 18 F-FDG, which is further released into the cytoplasm [20,21].Cossu et al. [22] showed that glucose processing mechanisms in the ER contribute to brain FDG uptake.Scussolini et al. [23] used a four-compartment model with ER for kinetic analysis of mouse breast cancer cells and confirmed that ER plays a key role in 18 F-FDG metabolism.Sommariva et al. [24] also showed that a four-compartment model with ER can also be used for 18 F-FDG kinetic analysis in mouse colon cancer.However, the role of the four-compartment model for estimating liver 18 F-FDG kinetics and distinguishing HCC remains unclear.
Liver kinetics require consideration of dual blood supplies from the hepatic artery and portal vein, and this study aimed to determine the following: (1) the availability of the dual-input four-compartment model with the endoplasmic reticulum (4C model) for liver and HCC kinetic analysis; (2) the differences in the corresponding kinetic parameters between the 4C model and the dual-input three-compartment (3C) model; (3) the role of the derived kinetic parameters for distinguishing HCC from background liver tissue; and (4) the HCC identifiability of the parametric images with the 4C model.

Patients
The Institutional Review Board of the First People's Hospital of Yun-nan Province approved this study (IRB number: KHLL2022-KY189).The 24 patients with HCC provided written informed consent to participate in the study; 21 males and 3 females were included.All patients underwent a 5-min dynamic PET/CT scan of the liver and a whole-body static PET/CT scan.A total of 28 pathologically diagnosed HCC lesions from 24 patients were analysed; 21 patients had a single HCC lesion, 2 patients had two HCC lesions, and 1 patient had three lesions.The long axis of these tumours ranged from 1.9 to 17.0 cm (mean 6.8 ± 3.5).

PET/CT acquisition
All HCC patients were scanned using a Philips Ingenuity TF PET/CT scanner (Cleveland, OH, USA) after they had fasted for at least 6 h and relaxed in a quiet room with low ambient light.

Dynamic PET/CT scan
A 5-min dynamic PET/CT scan was added before conventional PET/CT.A bolus injection was performed with 18 F-FDG (5.5 MBq/kg) in 2 mL of 0.9% saline, which was subsequently flushed with 20 mL of 0.9% saline at a flow rate of 2 mL/s.A liver CT scan (120 kV, 100 mA) was performed in a single bed, and the liver was in the centre of the scanner's field of view.For dynamic analysis, the images were divided into 16 frames: 5 s/ frame for the first 1 min (12 × 5 s) and 60 s/frame thereafter (4 × 60 s).

Conventional PET/CT scan
Conventional static scans were performed approximately 60 min after the 18 F-FDG push, and a whole-body CT scan (120 kV; 200 mA) was performed, including from the vertex of the skull to the proximal thigh, followed by a 1-min PET scan in each bed and a total of 11 beds.

Image analysis
The SUVmax was measured by delineating regions of interest (ROIs) on PET images following the methodology described in previous studies [11,25].Briefly, for lesions with imperceptible FDG uptake, ROIs were drawn relative to the conventional imaging findings.ROIs of the aorta and portal vein were placed at approximately two-thirds of the vascular cross-section.To compare HCC tumours to background tumour-free liver tissue, the respective ROIs were drawn in tumour-free liver tissue, and all the ROIs avoided blood vessels.

Kinetic modelling
In Fig. 1, the 4C model is compared to the 3C model.Figure 1A shows the 4C model, which accounted for the effect of the dual blood supply to the liver; the blood concentration of 18 F-FDG C B (t) , an input to the model, was calculated as the hepatic arterial 18 F- FDG concentration A(t) and portal venous 18 F-FDG concentration P(t): where HPI represents the hepatic artery perfusion index.C E (t) represents the concentra- tion of 18 F-FDG in liver tissue.C M (t) represents the concentration of phosphorylated 18 F-FDG-6-phosphate ( 18 F-FDG6P) in liver tissue.C R (t) represents the concentration of 18 F-FDG6P in the ER.K 1 is the rate constant for the transport of 18 F-FDG from blood to tissue by GLUT, and k 2 is the rate constant for removal.k 3 is the rate constant for the (1) phosphorylation of 18 F-FDG to 18 F-FDG6P, k 5 is the input rate of 18 F-FDG6P into the ER (by G6PT), and k 6 is the dephosphorylation rate of 18 F-FDG6P to 18 F-FDG (by G6Pase).
The compartment model is equivalently described by a set of ordinary differential equations [16]: The compact form of the IPE is given by: C T (t) is the output function of the kinetic model, which is the curve of tracer concentra- tion in the tissue as measured by PET/CT images over time.
For the 4C model (Fig. 1A), we have: where ( 2) For the 3C model (Fig. 1B), we have: Notably, the k 6 of the 4C model is comparable to the k 4 of the 3C model.

Parameter images
The aorta and portal vein were drawn as ROIs for an input function to the 4C model, and the formulas for calculating the parameters were as described above.Constrained by the fitting algorithm and kinetic model, we selected specific parameters of a patient whose lesion was detected via negative PET/CT images for pixel-by-pixel kinetic modelling.K 1 , k 3 , k 5 and HPI images were generated by performing 17 sequential frames of dynamic PET on a 144 × 144-pixel matrix image for each HCC patient.Pseudocolour was used for parameter images to display the calculated value in each pixel.The pseudocolour values for K 1 , k 3 and HPI were greater for HCC lesions than for background liver tissue and lower for k 5 .CT imaging was used to determine the exact location of the lesion.

Parameter estimation
With the rate constants as fit parameters, all model fits were performed according to the least-squares method, optimized with the Levenberg-Marquardt algorithm and implemented using MATLAB, R2019a (MathWorks, Natick, MA, USA).The unknown model parameter set of the 4C model is where WRSS(θ) represents the weighted residual sum of squares of the curve fit and w i represents the weighting factor of time frame N.

Statistical analysis
The TAC fit quality between the 4C model and the 3C model was compared using the Akaike information criterion (AIC) [26,27].Statistical analysis was performed using MedCalc version 13.0.0.0 (MedCalc software, Ostend, Belgium).Receiver operating characteristic (ROC) analysis was used to compare the kinetic parameters between HCC tissues and background liver tissues.The P values were calculated based on paired Student's t tests, and P < 0.05 indicated significant differences. (

TAC fit quality
The 4C model had a better fit quality with lower AIC values than did the 3C model for most patients, as shown in Table 1 and Additional file 1: Figure S1.An example of TAC fitting results for a patient with background liver tissue and HCC is shown in Fig. 2, with the 4C model fitting the data better than the 3C model.

Differences in the corresponding kinetic parameters between the 4C and 3C models
The differences in the corresponding kinetic parameters between the 4C and 3C models were compared, as shown in Table 2.

Comparison of kinetic parameters for distinguishing HCC from background liver tissue between the 4C and 3C models
The parameters obtained from the kinetic modelling analysis of liver 18 F-FDG PET/CT data using the 4C model and 3C model are shown in Table 3. K 1 , k 2 , k 3 and HPI were greater in HCC tissue than in background liver tissue (P = 0.019, P = 0.020, P = 0.022, P < 0.001) according to the 4C model, and k 6 and V b were not significantly different between diagnostic HCC and background liver tissue (P = 0.956, P = 0.127).Notably, k 5 from the 4C model was lower in HCC tissue than in background liver tissue (P = 0.006).V i and v were greater in HCC tissue than in background liver tissue (P = 0.032, P = 0.013).
k 3 , HPI and V b according to the 3C model were greater in HCC tissue than in background liver tissue (P = 0.021, P < 0.001, P < 0.001), and K 1 , k 2 and k 4 were not significantly different between HCC tissue and background liver tissue (P = 0.498, P = 0.080, P = 0.239).
The diagnostic performance of the top ten from high to low is A multiparametric ROC curve was used to compare the diagnostic performance of all the parameters of the 4C model and the 3C model.The AUC values of the multiparametric ROC curves of the 4C model and 3C model were 0.931 and 0.892, respectively.

Parameter images
The parameter images of K 1 , k 3 , k 5 and HPI of the 4C model were generated using the pixel-by-pixel method.Figure 3 shows a comparison of images from a 72-year-old In the 4C model, the parameter images for K 1 (Fig. 3C), k 3 (Fig. 3D), k 5 (Fig. 3E) and HPI (Fig. 3F) identified HCC (marked with arrows) in a patient who had negative findings on conventional metabolic PET/CT.

Discussion
This study preliminarily demonstrated the feasibility of the 4C model for short-term dynamic PET/CT in HCC patients.Compared with previous studies in which a 3C model was used to estimate 18 F-FDG metabolism in the liver [28,29], the 4C model has more kinetic parameters that can distinguish HCC from background liver tissue, and it provides additional kinetic parameters with diagnostic efficacy and, in addition, preliminarily generated parameter images to diagnose HCC.
Compared to static PET/CT imaging, dynamic PET/CT imaging with a kinetic model has the potential for use in all multiparameter quantitative imaging and more accurate metabolic information, and it is widely used for diagnosis [17,30,31].Dynamic PET protocols are less suitable for routine clinical application because of the longer scanning times, which can be too great of a burden to the patient.Liu et al. [5] performed kinetic modelling for different tissues or organs at 30, 45, and 75 min.Samimi et al. [32] proposed a short-term PET protocol using an early 5-min dynamic, supplemented by 3-min static imaging at 60 min postinjection.Based on the findings of previous studies and our clinical practice [11,25,33], a short-term protocol was used in this study, with 5-min dynamic PET supplemented by 1-min static imaging at 60 min postinjection; because of the metabolism of 18 F-FDG, static images were considered.
The three-compartment model describes the transport and phosphorylation of 18 F-FDG and is promising for differential diagnosis and therapeutic assessment of HCC.The development of cancer has further complicated the quantitative analysis of 18 F-FDG.G6P-phosphatase (G6Pase) is a complex of multiple proteins anchored to the ER lumen whose expression has been mostly characterized in the liver, kidney and gut; FDG6P is a recognized substrate for this enzyme, and its activity explains the relatively low sensitivity of 18 F-FDG PET/CT in hepatocellular carcinoma [34,35].The ER plays a crucial role in the activation of G6Pase, and 18 F-FDG6P and GP6 are transported via the transmembrane protein glucose-6-phosphate transporter (G6PT) into the ER, where hydrolysis produces free 18 F-FDG molecules that are released into the cytoplasm [22].
The experimental results of this study showed that the two models could fit the TAC well, and the 4C model showed better fit quality due to the greater number of parameters.The overall diagnostic efficacy of the 4C model was greater than that of the 3C model according to multivariate ROC analysis.
The liver has unique physiological features, as it has a dual blood supply from the hepatic artery and portal vein.HCC is supplied with most of its blood flow by the hepatic artery, which accounts for approximately 75-80%, whereas only 20-25% of normal liver tissue is supplied.Geist et al. [28] assessed the three-compartment model with different input functions, and the results showed that the kinetic parameters of the liver can be better estimated with a dual-input function.Wang et al. [18] used the SUVmean and SUVmax to model liver kinetics, and the proportion of hepatic arterial supply was greater in both HCCs than in normal liver tissue.We derive the portal vein input function directly from the image instead of from the spleen.First, 18 F-FDG exhibits a heterogeneous distribution in the arterial phase of the spleen.Second, the spleen contains both blood pool 18 F-FDG and metabolized 18 F-FDG.The results of the present study were consistent with those of previous studies in that the HPI was significantly increased in HCC patients in the 3C and 4C models, and the HPI in the 4C model was closer to the theoretical clinical value (0.836 ± 0.237 vs. 0.254 ± 0.286).
This study compared 4C and 3C models, which have similar biological significance and similar pharmacokinetic process parameters.The experimental results showed that the two models had similar transport and dephosphorylation rate constants and different removal and phosphorylation rate constants.K 1 is the rate of transport of 18 F-FDG from blood to tissue and is of great clinical importance.Wang et al. [15] showed that K 1 was able to assess liver inflammation in a staged manner.Zuo et al. [36] also showed the potential value of K 1 in assessing liver inflammation.The results of this study showed that K 1 expression is greater in HCC tissue than in background liver tissue in both models, which is due to the high expression of glucose transporter proteins in tumour cells.However, the 3C model of K 1 has no diagnostic efficacy.There was no significant difference in the K 1 values between the 4C model and the 3C model.Sommariva et al. [24] also reported similar estimates of K 1 for both models in a kinetic model of mouse colon cancer cells.
k 2 , a marker of clearing 18 F-FDG in tissue, was greater in HCC tissue than in background liver tissue in both models, and the 4C model showed significant differences.Notably, k 2 was not consistent between the two models, and that of the 4C model was lower than that of the 3C model for HCC and background liver tissue.The 4C model assumes that the endoplasmic reticulum is involved in the metabolism of 18 F-FDG and that the amount of free 18 F-FDG in the cytoplasm is reduced.
When 18 F-FDG enters tissues, hexokinase is phosphorylated to form 18 F-FDG-6P.Hexokinase is highly expressed in HCC, and k 3 is the phosphorylation rate.The results of this study showed that the k 3 values of the two models could both be used to distinguish HCC tissue from background liver tissue.However, their values were not consistent, with the k 3 of the 3C model being lower than that of the 4C model.Cossu et al. [22] demonstrated that ER metabolism may lead to further degradation of 18 F-FDG-6P.In the 4C model, 18 F-FDG-6P enters the endoplasmic reticulum through the transmembrane protein glucose-6-phosphate translocase, disrupting metabolic homeostasis in the cytoplasm, enhancing the catalytic activity of hexokinase, and producing more 18 F-FDG-6P to maintain a dynamic balance in the cell.
Glucose-6-phosphatase plays a critical role in maintaining blood glucose homeostasis, and it is highly expressed in the liver, which leads to the dephosphorylation of 18 F-FDG-6P.In contrast to that in the 3C model, 18 F-FDG-6P in the 4C model enters the ER (k 5 ), where it undergoes dephosphorylation and generates free 18 F-FDG, which is released into the cytoplasm.The results of this study showed that k 5 could be used to distinguish HCC tissue from background liver tissue, and background liver tissue values of k 5 were significantly greater than those in HCC tissue, indicating low expression of glucose-6-phosphatase in HCC.k 6 in the 4C model and k 4 in the 3C model represent the rate of dephosphorylation of 18 F-FDG-6P, and their values are basically the same, which is consistent with the results of previous studies [22,24].The rate of dephosphorylation is very low, but neglecting this parameter results in an underestimation of the 18 F-FDG metabolic rate.
The blood volume parameter V b can be measured using imaging methods [37]; however, this increases the complexity of PET imaging protocols and the radiation dose of 18 F-FDG.The results of this study showed that the V b of HCC tissue was greater than that of background liver tissue and were smaller with the 4C model.The 4C model includes extra compartments to account for more complex dynamics, such as differentiating between cellular and extracellular spaces or accounting for specific receptor-binding sites.These additional compartments may affect the estimation of Vb, making Vb appear smaller in the 4C model because the tracer distribution is accounted for in more compartments than in the 3C model.
Notably, in addition to k 5 , the 4C model also derives other kinetic parameters, namely, the volume fraction of interstitial V i and the ratio of ER to cytosolic volume v.The measurement of these two parameters is complicated, and they are taken as the estimation parameters in this paper.The experimental results indicate that, compared with background liver tissue, V i and v exhibit higher levels in HCC tissues.These findings could be used to distinguish HCC tissues from background liver tissue.These findings may be closely related to tumour growth and provide a theoretical basis for exploring the process of glucose uptake.
Due to the limitations of the fitting algorithm and model complexity, pixel-by-pixel calculations with multiple parameters are not applicable, and pixel-by-pixel dynamic modelling with specific kinetic parameters can better evaluate whole-liver uptake.Compared with other kinetic parameters, K 1 , k 3 , k 5 and HPI have more important clinical value.Therefore, we further performed pixel-by-pixel kinetic modelling in a patient with negative findings on conventional metabolic PET/CT to generate parametric images of four parameters using a 4C.Our results showed that the use of parametric images is helpful for visualizing quantitative parameters of whole-liver tracer kinetics and adds a new dimension to the existing conventional PET or PET/ CT images.
The present study has several limitations.First, the sample size of the dataset was small.Second, the reconstruction algorithm may affect the SUV [38]; however, further research into the use of the reconstruction algorithm is needed to improve the image quality of dynamic PET.Third, the pixel-by-pixel method takes a long time to generate parametric images, and further studies are needed to improve the fitting algorithm to increase the computational speed.Finally, due to practical and ethical considerations, kinetic analysis studies of lesion staging and drug treatments in human subjects are limited, and this topic will be the direction of future clinical tracer kinetics research.

Conclusion
In this study, we propose a 4C model with an endoplasmic reticulum for liver kinetics modelling via dynamic 18 F-FDG PET/CT imaging.The results showed that the 4C model performed better than the 3C model and produced additional useful parameters for kinetic estimation for differentiating HCC from background liver tissue, and the derived parameter images might be useful for diagnosing HCC.

Fig. 1
Fig. 1 Compartmental model for liver kinetic modelling.A The 4C model.B The 3C model

Fig. 2
Fig. 2 Examples of TAC fitting for two models.A TAC fitting for background liver tissue.B TAC fitting for HCC

Fig. 3
Fig. 3 The parametric images from the 4C model show hepatocellular carcinoma (arrow) with negative findings on conventional metabolic PET/CT.A CT image.B Conventional static PET/CT image.C Parameter image of K 1 .D Parameter image of k 3 .E Parameter image of k 5 .F Parameter image of HPI

Table 2
Differences in the corresponding kinetic parameters between the 4C model and 3C model

Table 3
Kinetic parameters estimated with the 4C model and 3C model male patient.CT image showing a slight decrease in opacity in the left lobe of the liver.Conventional static PET/CT images revealed negative results in the liver.