The elimination of ICG depends strongly on hepatic blood flow due to its high hepatic extraction-ratio (0.6–0.9 in healthy subjects Grainger et al., 1983). The extraction-ratio is the fraction of drug that is removed from the plasma after a single pass through the liver. The effect of varying hepatic blood flow on ICG-elimination has been studied by various groups. Kanstrup and Winkler (1987) found a strong positive correlation between hepatic blood flow and ICG-clearance when altering hepatic blood flow either pharmacologically or by food ingestion. Rowell et al. (1964) reported a strong positive correlation between changes in hepatic blood flow and ICG-clearance during exercise in healthy subjects but poor correlation in cirrhosis. Gadano et al. (1997) and Huet and Villeneuve (1983) studied the dependency of ICG-clearance on hepatic blood flow in cirrhotic and healthy subjects. Huet and Lelorier (1980) were interested in the effects of smoking and chronic hepatitis B reporting hepatic blood flow and ICG parameters.

Hepatic blood flow results from the interplay of various factors such as blood pressure, portal resistance and cardiac output. Further, it is often altered in disease (e.g., in portal hypertension Iwakiri, 2014) and after liver surgery (e.g., partial hepatectomy Kawasaki et al., 1991). As a consequence, accurate evaluation of liver function via ICG pharmacokinetics is challenging in diseases that affect systemic circulation (e.g., cardiac output) or hepatic blood supply. A better understanding of the effects of blood flow on ICG elimination would enable a more accurate evaluation of ICG liver function tests.

ICG is removed from the blood via transporter-mediated uptake into the hepatocytes. Two proteins on the sinusoidal membrane are mainly responsible for the hepatic uptake of ICG in humans, the organic anion transporting polypeptide 1B3 (OATP1B3, gene symbol: SLCO1B3) and the Na⁺-taurocholate cotransporting polypeptide (NTCP) (de Graaf et al., 2011; Kagawa et al., 2017). OATP1B3 is the major transporter for hepatic ICG uptake and subjects with a homozygous SLCO1B3 null allele show markedly impaired ICG clearance (Anzai et al., 2020).

The OATP level in hepatocytes has a large impact on plasma concentrations of various drugs (Schneck et al., 2004; Giacomini et al., 2010; Schipani et al., 2012). In human subjects, a large variability in the protein amount of OATP1B3 exists (Kimoto et al., 2012; Prasad et al., 2014; Burt et al., 2016). The OATP1B3 level does not depend on age or sex (Prasad et al., 2014) though some dependency on ethnicity has been reported (Peng et al., 2015).

ICG is bound to plasma proteins (serum albumin and lipoproteins) (Kamisaka et al., 1974; Ott, 1998). It has been suggested that these plasma proteins are involved in the hepatic uptake mechanism of ICG at the sinusoidal membrane (Berk et al., 1987; Shinohara et al., 1996). However, no consensus about the effect of plasma proteins on ICG uptake has been reached. In contrast, the effect of bilirubin on ICG uptake has been extensively studied. Bilirubin is an end product of heme degradation which is primarily located in the blood and is almost completely bound to albumin (Fevery, 2008; Maruhashi et al., 2019). Significant negative correlation between ICG elimination and plasma bilirubin levels has been reported (Paumgartner et al., 1969; Branch et al., 1976). Changes in bilirubin plasma levels are often induced by hepato-biliary diseases, with the prime example being Gilbert's disease (Fretzayas et al., 2012). Further, increased bilirubin plasma levels can be caused by biliary obstruction or viral hepatitis and are used as an indicator of acute liver failure (Sullivan and Rockey, 2017).

An important question for the individualized and stratified evaluation via DLFTs is how factors such as body weight, age, and sex affect the elimination of the test substance. As summarized by Kim et al. (2015), age has a significant effect on liver volume, blood flow, and function. A reduction of functional liver mass, total liver volume, and a decrease in hepatic blood flow are the most relevant age induced changes to the liver. Additionally, the susceptibility to liver disease increases with age accompanied by a decline in the hepatic regenerative response which has substantial consequences for liver surgery (Schmucker, 2005). Reduced ICG clearance with increasing age has been reported by Wood et al. (1979). Liver volume and body weight have been shown to correlate well in western adults (Vauthey et al., 2002). Due to the dependency of ICG elimination on liver volume (Roberts et al., 1976), body weight is an important factor to be considered in the evaluation of liver function with ICG. Because of significant differences in average body weight and organ volumes between male and female subjects, sex is another important factor in the analysis of variability in ICG liver function tests. However, Martin et al. (1975) reported no variations in ICG-clearance per kg body weight between male and female subjects, while reporting significantly increased ICG-PDR in women.

Within this work we systematically investigated the individual contribution of these factors to the large inter-individual variability in liver function tests based on ICG using a recently developed and validated physiologically based pharmacokinetics (PBPK) model of ICG (Köller et al., 2021).

Parameter scans (Figure 2) were performed by varying the model parameters corresponding to the relative change in hepatic blood flow f_bloodflow [-], relative change in cardiac output f_{cardiac_output} [-], relative change in OATP1B3 amount f_oatp1b3, liver volume FVli [l/kg], body weight BW [kg], and plasma bilirubin concentration bil_ext[-]. The parameter values of the unchanged model are indicated as reference in the plots. For the relative changes f_bloodflow, f_{cardiac_output}, and f_oatp1b3 the reference parameter value is 1.0 [-]. Bilirubin scans were performed on a log scale whereas all other scans were performed on a linear scale. Most simulations were performed for four different cirrhosis degrees by varying the f_cirrhosis parameter. This parameter determines the fraction of lost liver tissue and shunted blood around the liver. Values of f_cirrhosis used for the simulations of controls, mild, moderate and severe cirrhosis are 0.0, 0.40, 0.70, and 0.81, respectively.

For the analysis of variability in ICG pharmacokinetics, a large dataset of in silico individuals was created (see Figure 5). Age, body weight, sex, height, and ethnicity were based on subjects sampled from the National Health and Nutrition Examination Survey (NHANES) spanning the years 1999–2018 (NHANES, 1999-2018). Due to the sampling from a real cohort it was possible to account for the covariances between the respective variables. Children and adolescents (age <18 years), obese subjects (BMI > 30), and subjects with age ≥ 85 from 1999 to 2006 and ≥ 80 from 2007 to 2018 (due to top coding in NHANES at 85 and 80 years, respectively) were excluded. The resulting 35,427 subjects were oversampled to reach 100,000 individuals. This ensured sufficient samples in all stratified subgroups. Based on the age of a given individual, liver volume and hepatic blood flow were determined by multivariate sampling of liver volume per body weight and hepatic blood flow per body weight from the respective age distribution and subsequent multiplication with the individual body weight. This allowed to account for the covariances between liver volume and blood flow as well as the dependency of age. The normal distributions and covariance-matrices used for the sampling were calculated from data from Wynne et al. (1989). The transport protein amount (OATP1B3) was sampled independently from a lognormal distribution that was fitted to data from Peng et al. (2015). The OATP1B3 distribution was assumed age and sex independent as reported by Prasad et al. (2014). Individual model simulations were performed by adjusting the model parameters corresponding to individual body weight BW [kg], liver volume FVli [l/kg], hepatic blood flow f_bloodflow [-], and amount of OATP1B3 f_oatp1b3 [-]. The scaling factors f_bloodflow and f_oatp1b3 describe the relative change from the model reference state. Individual ICG liver function test simulations were performed by administering 0.5 [mg/kg] ICG to the respective virtual individual and calculating the pharmacokinetics parameters on the resulting time course.

The systemic blood flow of the PBPK model is based on the cardiac output, which is scaled by the body weight. The liver is perfused through a dual blood supply consisting of arterial blood from the hepatic artery and venous blood from the portal vein. All organs besides the liver, the gastrointestinal tract, and the lung were pooled into the rest compartment. The included hepatic metabolism and biliary excretion are depicted in Figure 1B. ICG is imported in the liver via OATP1B3. Hepatic ICG is exported through the bile and subsequently excreted via the feces. The effect of bilirubin on hepatic ICG uptake was modeled as a competitive inhibition based on the assumption that ICG can only be eliminated from the plasma if bound to plasma proteins. Due to the sequestration of plasma proteins bilirubin acts as a competitive inhibitor of ICG elimination, as both substances compete for plasma protein binding sites. Plasma bilirubin levels change slowly compared to the timescale of ICG liver function tests (about 15 min) and were therefore assumed in steady-state. Liver cirrhosis was modeled by a combination of functional tissue loss and shunts. For a detailed description of the model we refer to Köller et al. (2021).

First a systematic analysis of the effect of physiological variation on ICG parameters was performed (see Figure 2). Specifically, the dependency of ICG-clearance, ICG-PDR, ICG-R15 and ICG-t_1/2 on hepatic blood flow, cardiac output, transport protein amount (OATP1B3), liver volume, body weight, and plasma bilirubin was analyzed. An increase in all physiological factors except the plasma bilirubin concentration results in an increase in ICG elimination (increased ICG-PDR and ICG-clearance, reduced ICG-R15 and ICG-t_1/2). Changes in blood flow, OATP1B3 level, and liver volume have similar nonlinear effects on ICG parameters, whereas the body weight has an almost linear effect on ICG-clearance but only minimal effects on the other parameters. In the model, liver volume (tissue and blood vessels) are scaled with the body weight. As a result the plasma volume which is cleared from ICG every minute (clearance) increases with the body weight, without any change to the plasma disappearance rate, retention ratio or half-life.

Mild, moderate and severe cirrhosis reduce ICG elimination (decreased ICG-clearance and ICG-PDR, increased ICG-R15 and ICG-t_1/2) in a stepwise fashion without changing the overall curve shapes. This reduction is reflected by the clinical data, due to a loss of function in liver cirrhosis. As a result of their calculation, ICG-t_1/2 and ICG-PDR (kel·100%) show inverse behavior when ICG-elimination is altered (t_1/2 = ln(2)/kel). The model predictions under the assumption that cirrhosis can be described as a combination of reduced functional liver volume and shunting of blood around the liver (see Köller et al., 2021 for details) are in good agreement with the data.

Model predictions were validated with data from multiple publications. An overview over all data sets used is provided in Table 1. For the dependencies on physiological factors clinical data sets from healthy controls and subjects with mild, moderate and severe cirrhosis corresponding to Child-Turcotte-Pugh (CTP) classes A, B, and C, respectively, were used (see Figure 2: ICG-clearance, ICG-PDR, ICG-R15, and ICG-t_1/2 depending on hepatic blood flow (Skak and Keiding, 1987; Grundmann et al., 1992; Møller et al., 1998, 2019; Pind et al., 2016); ICG-clearance, ICG-R15 and ICG-t_1/2 depending on cardiac output (Grundmann et al., 1992; Pind et al., 2016); ICG-PDR and ICG-R15 depending on OATP1B3 (Namihisa et al., 1981; Kagawa et al., 2017; Anzai et al., 2020); ICG-clearance, ICG-PDR, and ICG-R15 depending on liver volume (Roberts et al., 1976; Hashimoto and Watanabe, 2000; Haimerl et al., 2016); ICG-clearance and ICG-PDR depending on body weight (Huet and Villeneuve, 1983; Haimerl et al., 2016). The model predictions show very good agreement with the validation data.

Additional validation of the model predictions were performed for the dependency of ICG parameters on blood flow (see Figure 3) and plasma bilirubin (see Figure 4).

Figures 3A,B show the relation between ICG-clearance and hepatic blood flow in healthy subjects and patients of liver cirrhosis. ICG-clearance is reduced in liver cirrhosis. The simulations were performed for healthy controls and three different degrees of cirrhosis (mild, moderate, severe) and are in good agreement with the clinical data (Huet and Lelorier, 1980; Huet and Villeneuve, 1983; Gadano et al., 1997). Figure 3C shows the change in ICG-clearance due to an externally induced change in hepatic blood flow by exercise, food ingestion or pharmacological intervention (Kanstrup and Winkler, 1987) with the corresponding model simulation. The relation is predicted accurately by the model, with an increase in blood flow resulting in an increased clearance of ICG. In Figure 3D the dependency of the ICG extraction ratio on the hepatic blood flow is depicted. With increasing hepatic blood flow the extraction ratio decreases with model predictions for healthy and cirrhotic subjects being in good agreement with the data (Leevy et al., 1962).

The bilirubin plasma concentration in healthy subjects shows little variation (Figures 4A–C,E,F). However, in liver cirrhosis and other liver diseases bilirubin levels may vary by an order of magnitude and are generally increased. The simulations depicted in Figure 4 were performed for healthy controls and three different cirrhosis degrees based on the assumption of competitive inhibition of ICG uptake by bilirubin. Results were compared to clinical data of control and diseased subjects. Figure 4 shows the dependency of ICG parameters on the plasma bilirubin levels (Figures 4A,B: ICG-clearance; Figure 4C: ICG-kel; Figure 4D: ICG-R15; Figure 4E: ICG-R20; Figure 4F: ICG extraction ratio). Overall the decrease in ICG elimination due to elevated bilirubin plasma levels is predicted accurately. The simulations for healthy controls agree well with the data in healthy subjects.

In summary, model predictions for the effect of hepatic blood flow, cardiac output, OATP1B3 level, liver volume, body weight and bilirubin on ICG parameters could be validated with a large set of studies in healthy controls and various degrees of cirrhosis spanning almost 60 years of clinical research (Caesar et al., 1961; Leevy et al., 1962, 1967; Branch et al., 1976; Roberts et al., 1976; Huet and Lelorier, 1980; Namihisa et al., 1981; Huet and Villeneuve, 1983; Kanstrup and Winkler, 1987; Skak and Keiding, 1987; Kawasaki et al., 1988; Grundmann et al., 1992; Gadano et al., 1997; Møller et al., 1998, 2019; Hashimoto and Watanabe, 2000; D'Onofrio et al., 2014; Haimerl et al., 2016; Pind et al., 2016; Kagawa et al., 2017; Anzai et al., 2020).

To analyze the inter-individual variability of ICG parameters, in silico ICG liver function tests were performed for 100,000 subjects (Figure 5. For every individual the age, body weight, sex, height and ethnicity was based on the NHANES cohort with subsequent sampling of age-dependent liver volume and hepatic blood flow and OATP1B3 amount. The 35427 NHANES subjects were oversampled to 100,000 subjects, i.e., every subject occurred around three times with different liver volume and hepatic blood flow samples. By sampling from a large cohort of real individuals the covariances between the parameters age, body weight, sex, height and ethnicity could be accounted for. In silico ICG liver function tests used a dose of 0.5 [mg/kg] ICG (Figure 5A). The dependency of the body weight on the age in men and women in the simulated population are depicted in Figures 5B,C, respectively. In general, women have a lower body weight. Both distributions show an increase in body weight up until 40–60 year, followed by a decline in older ages. The number of subjects in younger age-groups is higher than in older age-groups, although this might not be representative of the population, but rather of the NHANES study design.

For every virtual individual the OATP1B3 level was sampled from a lognormal distribution based on reported protein concentrations by Peng et al. (2015) (see Figure 5D). OATP1B3 samples were assumed to be independent of age, body weight, sex, height and ethnicity.

For every virtual individual the age-dependent liver volume and hepatic blood flow were sampled under consideration of the underlying covariances between hepatic blood flow per kg body weight and liver volume per kg body weight, based on data by Wynne et al. (1989) (Figures 5E–G). Both liver volume and hepatic blood flow per body weight decrease with increasing age. Age dependent multivariate sampling was used to determine hepatic blood flow and liver volume for every virtual individual, i.e., samples were taken from the respective age-dependent distribution.

The inter-individual variability in ICG elimination was analyzed by performing an individualized ICG test simulation for each of the n = 100,000 subjects. ICG parameters were calculated from the individual ICG time courses. To analyse the effect of age, body weight and sex on ICG elimination the population was stratified by age (18–40 year, 41–65 year, and 66–84 year), body weight (40–60 kg, 60–80 kg, 80–100 kg, and 100–140 kg), and sex (M, F). ICG clearance, PDR, R15, and t_1/2 for each subgroup are shown in Figure 6. With increasing age (independent of body weight), ICG elimination is reduced, as reflected by a decrease in clearance and PDR and an increase in ICG-R15 and t_1/2. With increasing body weight ICG clearance increases whereas PDR, R15 and t_1/2 show no change. Variation in body weight has a much larger effect on ICG-clearance, than on any other PK parameter in line with Figure 2E.

Differences between the sexes are marginal in all parameters after stratification for body weight and age. Due to the lower body weight of women as depicted in Figures 5B,C and the body weight dependency of ICG clearance an apparent difference between male and female ICG-clearance can be observed in the unstratified data.

The corresponding dependencies in mild cirrhosis, moderate cirrhosis, and severe cirrhosis are depicted in Supplementary Figures 1–3, respectively. Similar to healthy subjects, ICG elimination is reduced in cirrhosis with increasing age, as reflected by a decrease in clearance and PDR and an increase in ICG-R15 and t_1/2. With increasing cirrhosis degree ICG clearance and PDR decrease and R15 and t_1/2 increase, in line with Figure 2.

To validate the results of the population model predictions (Figure 6) multiple comparisons to clinical data sets were performed (Figures 7, 8).

The predicted dependency of ICG-clearance and ICG-kel on age in the in silico population in Figure 7 is in very good agreement with data for healthy controls (Caesar et al., 1961; Branch et al., 1976; Wood et al., 1979; Kawasaki et al., 1988), and cirrhosis (Caesar et al., 1961; Branch et al., 1976; Jost et al., 1987; Kawasaki et al., 1988). ICG-clearance and ICG-kel decrease with increasing age and with increasing cirrhosis degree. The clinical data for cirrhosis did not provide any information on the disease severity such as CTP scores, so that cirrhosis data is plotted for all simulated severities. The model predictions cover the complete range of reported ICG-clearance and ICG-kel in cirrhotic subjects.

For additional validation, the population variability in the dependency of ICG parameters on hepatic blood flow was studied in Figures 8A–D) (corresponding to Figure 3).

Figures 8A,B show the effect of inter-individual differences on the dependency of ICG-clearance on hepatic blood flow. The resulting variability especially in the control samples (gray area), is very large emphasizing the importance of including confounding factors in the evaluation of liver function.

Figure 8C shows the change in ICG-clearance when hepatic blood flow is changed either by exercise, food ingestion or by pharmacological intervention. By including the inter-individual differences in the simulation, we were able to predict the variability in this dependency accurately. From the clinical data, we assume however, that the external influences, that were used to alter hepatic blood flow, had additional effects on ICG elimination, because even subjects with unchanged hepatic blood flow showed a decrease in clearance. It would be of high interest to analyze what these effects might be. This also shows, that recent food ingestion and long-term medication that affects blood flow are additional factors that have to be considered in liver function evaluation with ICG.

Figure 8D shows the relation between the ICG extraction ratio and the hepatic blood flow. The changes in extraction ratio are in good agreement with the clinical data, but the simulations taking inter-individual variability into account cover a much larger range of blood flow per body surface area than the data.

Next, the inter-individual variability in the correlations between ICG parameters in healthy and cirrhotic subjects were simulated (Figures 8E–H). The corresponding results without variability have been published previously (Köller et al., 2021).

Interestingly, all variability in the correlation between ICG-R20 and ICG-t_1/2 as well as ICG-R20 and ICG-kel lies on a nonlinear relationship (see Figures 8E,F). Moreover, the clinical data follows the same nonlinear dependencies. Because all PK parameters of a subject are calculated from the same plasma disappearance curve, the results follow a strict nonlinear relationship.

In Figure 8G the correlation between ICG-PDR after ICG doses of 0.5 mg/kg and 5.0 mg/kg is depicted. The relation is mostly linear, however some variation is observed, which agrees very well with the clinical data. This suggests a small dose-dependency of ICG-PDR depending on individual subject properties. In a previous analysis we could not find any dose-dependency of ICG-PDR for the model with reference parameters (Köller et al., 2021). A more detailed investigation into the factors causing the PDR dose dependency would be highly relevant.

A linear correlation, without deviation due to inter-individual differences, is observed between ICG-clearance calculated after a bolus administration and during a constant intravenous infusion of ICG (see Figure 8H) with the clinical data following the same linear dependency.

Finally, we were interested in the contribution of individual factors to the observed population variability Figure 9 using a data set of ICG-clearance and ICG-PDR by Sakka and van Hout (2006). The predicted variability between ICG-clearance and ICG-PDR in the in silico population is in very good agreement with the observed variability in the data (Figure 9A). The combined effect of variation in hepatic blood flow, OATP1B3 amount, liver volume and body weight predicts the variability in the clinical data very accurately.

To study the individual contribution of each of the above-mentioned factors these factors were varied individually while setting the remaining factors to their reference values (Figures 9B–E). Hepatic blood flow, OATP1B3 amount, and liver volume affect ICG-clearance and PDR in a similar manner resulting in a linear dependency. Compared to the model's reference simulation, these factors are able to increase as well as reduce ICG elimination. The individual effects appear to be additive as none of them individually can achieve the complete range of variability that is observed when they are varied together (Figure 9A). In contrast, the body weight has a much smaller effect on ICG-PDR than on ICG-clearance thereby spanning an alternative axis of variation. Specifically, it is the main source of deviation from the correlation line between PDR and clearance.