Concentrations and pharmacokinetic parameters of MRI and SPECT hepatobiliary agents in rat liver compartments

Background In hepatobiliary imaging, systems detect the total amount of agents originating from extracellular space, bile canaliculi, and hepatocytes. They add in situ concentration of each compartment corrected by its respective volume ratio to provide liver concentrations. In vivo contribution of each compartment to liver concentration is inaccessible. Our aim was to quantify the compartmental distribution of two hepatobiliary agents in an ex vivo model and determine how their liver extraction ratios and cholestasis (livers lacking canalicular transporters) might modify it. Methods We perfused labelled gadobenate dimeglumine (Bopta, 200 μM, 7% liver extraction ratio) and mebrofenin (Meb, 64 μM, 94% liver extraction ratio) in normal (n = 18) and cholestatic (n = 6) rat livers. We quantified liver concentrations with a gamma counter placed over livers. Concentrations in hepatocytes and bile canaliculi were calculated. Mann-Whitney and Kruskal-Wallis tests were used. Results Hepatocyte concentrations were 2,043 ± 333 μM (Meb) versus 360 ± 69 μM (Bopta, p < 0.001). Meb extracellular concentrations did not contribute to liver concentrations (1.3 ± 0.3%). The contribution of Bopta extracellular concentration was 12.4 ± 1.9% (p < 0.001 versus Meb). Contribution of canaliculi was similar for both agents (16%). Cholestatic livers had no Bopta in canaliculi but their hepatocyte concentrations increased in comparison to normal livers. Conclusion Hepatocyte concentrations are correlated to liver extraction ratios of hepatobiliary agents. When Bopta is not present in canaliculi of cholestatic livers, hepatocyte concentrations increase in comparison to normal livers. This new understanding extends the interpretation of clinical liver images.


Background
The quantification of liver function in cirrhotic patients is important to evaluate the tolerance to partial hepatectomy and estimate prognosis. Besides various plasma biomarkers, imaging with hepatobiliary agents is another option to quantify liver volume and function [1][2][3][4]. The function is quantified by imaging parameters such as the maximum liver enhancement or activity, the time to obtain the maximal signal, and the elimination half-life of agents from livers [5][6][7].
Several hepatobiliary agents such as gadobenate dimeglumine (Bopta), gadoxetic acid, and mebrofenin (Meb) are transported inside hepatocytes across the sinusoidal Organic anion transporting polypeptide (Oatp). To efflux from hepatocytes, agents cross the Multidrug resistance associated protein 2 (Mrp2) located on the canalicular membrane and Mrp3 on the sinusoidal membrane. Hepatocyte concentrations reflect the balance between these uptake and excretory transporter activities. When Oatp disappears in advanced hepatocellular carcinoma, the tumour appears hypointense on hepatobiliary phase in comparison to surrounding hepatocytes that retain sinusoidal transporters [8][9][10]. Besides hepatocytes, imaging also relies on concentrations inside the extracellular compartment and bile canaliculi. However, this compartmental distribution (or contribution of each compartment to liver concentrations) is inaccessible in vivo.
Hepatobiliary imaging detects the total amount of agents originating from the extracellular space, bile canaliculi, and hepatocytes. The system adds the in situ concentrations of each compartment corrected by its respective volume ratio to liver to provide liver concentrations [11]. Thus, in cirrhotic livers, parenchymal hypointensity on hepatobiliary phase reflects the increased volume ratio of the extracellular space when fibrosis replaces hepatocytes. The hepatocyte volume decreases and in situ hepatocyte concentrations are impaired by the low expression of Oatp [12,13]. Volume ratio of bile canaliculi to liver and in situ concentrations are unknown in cirrhosis.
The isolated and perfused rat liver is an ex vivo model of pharmacokinetic research which can quantify the compartmental distribution of transporter-dependent hepatobiliary imaging [14]. Hepatobiliary agent concentrations are measured in hepatic veins and common bile duct. By placing a gamma counter over livers, it is possible to mimic an imaging system and quantify liver concentrations during the perfusion of Bopta or Meb. A preperfusion of gadopentetate dimeglumine (Dtpa) quantifies the extracellular concentrations, whilst concentrations in bile canaliculi are calculated from bile concentrations and the volume ratio of canaliculi to liver [15].
The aim of our study was to quantify the compartmental distribution of two hepatobiliary agents in an ex vivo model and determine how their liver extraction ratios and cholestasis (livers lacking canalicular transporters) might modify it. From the accumulation and decay profiles of hepatocyte concentrations, new pharmacokinetic parameters will be described to better understand hepatobiliary images.

Isolated and perfused rat livers
A total of 24 livers were evaluated. Livers from 18 normal male Sprague-Dawley rats were isolated and perfused under anaesthesia (Pentobarbital, 50 mg kg −1 , i.p.). The protocol was carried out in accordance with the Swiss Guidelines. It was accepted by the institutional ethical Committee (University of Geneva) and approved at the veterinary office in Geneva (No. 1006/3384). We also perfused Bopta in six cholestatic rats lacking Mrp2 [16].
The abdominal cavity was opened, and the portal vein was cannulated [17]. The abdominal vena cava was transected and an oxygenated Krebs-Henseleit-bicarbonate (KHB) solution was pumped into the portal vein, the solution being discarded by a vena cava transection. The liver flow rate (Q H ) was slowly increased up to 30 mL/min. A cannula was inserted in the right atrium and the abdominal inferior vena cava ligated, allowing solutions perfused through the portal vein to efflux by hepatic veins.
Livers were perfused with KHB solution ± imaging agents using a nonrecirculating system: livers were perfused with fresh solutions and solutions flowing from hepatic veins were discarded (Fig. 1c). The common bile duct was cannulated to collect bile samples and measure bile concentration (C bile , μM) and bile flow rate (Q bile , μL/min/liver) every 5 min. Agent concentrations in hepatic veins (C out , μM) were collected every 5 min.
We diluted agents in the KHB solution that contain 118 mM NaCl, 1 Nine normal livers were perfused with Technescan Dtpa® (Dtpa, b.e.imaging GmbH) and mebrofenin (Meb; Choletec®; Bracco Imaging). Dtpa and Meb (25 mg) were labelled with the same radiotracer 99m Tc (7 and 11 MBq, respectively). Both solutions are commercially available for patients. Dtpa distributes only in the extracellular compartment whilst Meb distributes in the extracellular space, hepatocytes, and bile canaliculi. Both agents were diluted to a 64-μM concentration. Dtpa and Meb perfusion were followed by a rinse period with KHB solution. The protocol period lasted 105 min.
To quantify agent concentrations in liver compartments, a gamma counter that collects count rates every 20 s was placed 1 cm above a right liver lobe. At the end of experiment, Bopta or Meb liver amounts were measured by an activimetre and related to the last count rates. Bopta or Meb concentrations in the common bile duct and hepatic veins were measured with a gamma counter. Concentrations in large vessels, bile ducts, and livers are expressed in μM units. We considered that 1 g of liver was close to 1 mL.
Calculation of hepatocyte concentrations (Fig. 1c) The gamma counter delineated a region of interest from which Bopta or Meb amounts originating from the extracellular, bile canaliculi, and hepatocyte compartments were divided by the rat liver weight to obtain liver concentrations (C liver , μM). Concentrations in the extracellular compartment (C EC , μM) were constant during the perfusion of Dtpa. The concentrations detected by the counter were similar to the in situ C EC because the distribution volume is 1. We assumed that concentrations inside the bile canaliculi were similar to those measured in the common bile duct (C bile , μM). The concentrations of bile canaliculi detected by the counter (C BC ) were C bile · 0.0043 according to Blouin et al. [20] who measured the volume ratio of bile canaliculi to liver in rat biopsies. The hepatocyte concentrations (C HC78% ) detected by the counter were equal to C liver − C EC − C BC and originate from 78% of the liver volume according to Blouin et al. [20]. To convert C HC78% measured by the counter into in situ concentration into hepatocytes (C HC100% ), we applied the equation: C HC100% = (100/78) × C HC78% .

Profiles of liver concentrations over time
To analyse Bopta or Meb liver accumulation over time, we searched for nonlinear regressions that fit the data using the GraphPad Prism software (version 8, Graph-Pad Software, La Jolla CA, USA). In normal livers, data fitted either a continuous hinge function (segmental regression lines with gentle connexion) [21] or a segmental linear regression with abrupt connexion [22]. Both regressions were described by two lines L 1 and L 2 intersecting at T 0 (min) or time when bile excretion starts to impact the accumulation. Before T 0 , the slope of L 1 ( slope L 1,liver in μM/min) characterises Bopta or Meb uptake into hepatocytes across Oatp. After T 0 , the slope of L 2 ( slope L 2,liver in μM/min) characterises the balance between entry and efflux transporter activities.
During the rinse period, no agent enters into liver and concentration decay fitted a one-phase decay Y = (Y 0 − plateau) · e −kel · X + plateau. The software provided a decay (elimination) rate constant (k el,liver in min −1 ) and a half-time (T 1/2,liver in min) or time to reach 50% of the initial concentrations. With the assumption that the hepatocyte volume (V HC , mL) was 78% of liver weight, the elimination clearance from hepatocytes (CL el,HC in mL/min) was calculated by CL el,HC = k el,HC × V HC .
Liver concentrations were acquired every 20 s by the counter but this acquisition frequency is difficult to implement in clinical imaging. Therefore, we simulated decreased acquisition frequencies (2, 5, and 10 min) and determined the lower frequency that gives T 0 , slope L 1,liver , slope L 2,liver , and k el,liver similar to those obtained at a 20-s acquisition frequency.

Profiles of hepatocyte concentrations over time
Liver pharmacokinetic parameters do not fully characterise the transporter functions of hepatocytes because liver concentrations also include extracellular and canaliculi concentrations. Consequently, we measured all parameters using hepatocyte concentrations and compared them to those obtained in livers.

Statistical analysis
Data are given as means ± SD. To compare Bopta or Meb parameters and to determine the influence of Mrp2 absence on Bopta parameters, we used a Mann-Whitney test (GraphPad Prism version 8, GraphPad Software, San Diego, USA). To compare the effect of acquisition frequencies on pharmacokinetic parameters, we used a Kruskal-Wallis test with multiple comparisons between frequencies. Difference between groups was considered significant for p < 0.05.  Table 1 describe how liver extraction ratios and cholestasis interfere with the compartmental distribution of hepatobiliary agents. Meb has a 94% liver extraction ratio and provided much higher maximal C HC78% (2,043 ± 333 μM) than Bopta (360 ± 69 μM, p < 0.0001) which has a 7% liver extraction ratio. Consequently, Meb C out in hepatic veins was low, whilst Bopta C out was only slightly lower than the perfused concentrations (Table 1). Meb concentrations in the extracellular space did not contribute much to liver concentrations (Table 1, 1.3 ± 1.9%). The maximal Meb concentrations detected by the counter in bile canaliculi (C BC ) were 393 ± 61 μM and accounted for 17 ± 4% of liver concentrations. In contrast, maximal Bopta C EC (60 ± 10 μM) participated to liver concentrations all along the accumulation period (12.4 ± 1.9%, p < 0.001 versus Meb). Maximal Bopta C BC was 66 ± 11 μM and accounted for 14 ± 4% (no difference with Meb, p = 0.09). The lack of Mrp2 in cholestatic livers induced low Bopta C BC , increased Bopta accumulation in hepatocytes, and Bopta hepatocyte trapping during the decay period ( Fig. 2c and Table 1).

Accumulation and decay profiles of Bopta and Meb liver concentrations
Bopta liver accumulation fitted a segmental linear regression, whilst Meb accumulation fitted a continuous hinge function (Fig. 3a, b, left panels). Both regressions were described by two lines L 1 and L 2 intersecting at T 0 or time when bile excretion started to impact the accumulation. A gentle transition between the two lines characterised Meb (Fig. 3b, left panels, red fit), whilst Bopta transition was abrupt (Fig. 3a, left panel, red fit). T 0 was slightly shorter for Meb (5.5 ± 1.1 min) than Bopta (8.0 ± 0.5 min) (p < 0.001, Table 2). The first lines (L 1 ) below T 0 had a slope of 37 ± 5 μM/min for Bopta and 333 ± 71 μM/min for Meb (p < 0.001). Thus, Meb entry into livers was much higher than Bopta entry. The second lines (L 2 for time > T 0 ) had lower slopes (8 ± 1 μM/min for Bopta and 16 ± 5 μM/min for Meb, p < 0.001). After T 0 , liver concentrations reflected the balance between uptake and excretory transporter activities. Bile concentrations were detectable 5 min after the perfusion start: 13,994 ± 2,391 μM for Meb and 2,107 ± 710 μM for Bopta (p < 0.001). During the rinse period, Bopta and Meb decay of liver concentrations  fitted a one-phase decay (Fig. 3a, b, right panels) with a higher k el,liver for Meb (0.13 ± 0.02 min −1 ) than for Bopta (0.09 ± 0.01, p < 0.001, Table 2). In livers lacking Mrp2, Bopta accumulation fitted a single linear regression (L) during the entire perfusion period (Fig. 3c, left panel). T 0 value was not available and Bopta bile excretion was minor. The L slope (28 ± 6 μM/min) was significantly lower than the L 1 slope measured in normal livers (37 ± 5 μM/min, p = 0.01), showing a decreased Bopta entry in cholestatic livers. There was no decay during the rinse period and Bopta remained trapped inside hepatocytes.

Accumulation and decay profiles of Bopta and Meb hepatocyte concentrations
All pharmacokinetic parameters were also measured in hepatocytes to eliminate the impact of the extracellular and canaliculi compartments on the results. In hepatocytes, both Bopta and Meb accumulation fitted a continuous hinge function during the perfusion period (data  (Table 2). L 1 and L 2 slopes were significantly lower for Bopta than for Meb. During the decay period, the decline of hepatocyte concentrations fitted a one-phase decay with a k el,HC higher for Meb than for Bopta ( Table 2). The elimination clearance from hepatocytes (CL el,HC ) was significantly higher for Meb than Bopta.

Parameter comparisons between liver and hepatocytes
Despite small discrepancies, liver and hepatocyte parameters were close. Bopta and Meb T 0,liver was longer than the respective T 0,HC (Table 2). Bopta and Meb L 1,liver slopes were lower than L 1,HC slopes. L 2,liver and L 2,HC slopes were identical for both agents. Bopta k el were similar in hepatocytes and livers. Meb k el was slightly higher in hepatocytes than in livers.

Effect of acquisition frequency on pharmacokinetic parameters
To allow more easy translation to clinical imaging, we determined the lower acquisition frequency that gives pharmacokinetic parameters similar to those measured with a 20-s frequency (Fig. 4). Similar Bopta and Meb T 0 and L 1 slopes were obtained with acquisition frequencies of 20 s, 2 min, and 5 min. Bopta and Meb decay parameters were similar from 20 s to 10 min (data not shown).

Discussion
Our study describes how liver extraction ratios and cholestasis interfere with the compartmental distribution of hepatobiliary agents. Meb provides much higher maximal liver concentrations than Bopta, with hepatocytes contributing to 78% of liver concentrations [20]. Meb in the extracellular compartment does not contribute much to liver concentrations, whilst Bopta in the extracellular compartment participates to liver concentrations all along the accumulation period. The contribution of bile canaliculi to liver concentrations (close to 16%) is similar for both agents. Thus, Meb liver concentrations mainly rely on hepatocytes and bile canaliculi, whereas Bopta liver concentrations also depend on the extracellular compartment. In comparison to Bopta, Meb chemical structure has a huge affinity for the sinusoidal transporter Oatp. The second hepatobiliary MR agent gadoxetic acid which is widely used in clinical liver imaging has a higher liver extraction ratio than Bopta and its liver pharmacokinetics should be intermediate between Meb and Bopta [23][24][25].
In livers lacking Mrp2 and perfused with Bopta, liver concentrations only rely on the hepatocyte and extracellular compartments. The low Bopta concentrations in bile canaliculi were associated with higher hepatocyte concentrations in comparison to normal livers. This increased hepatocyte accumulation does not depend on Bopta hepatocyte uptake which is decreased. Indeed, the L slope during Bopta accumulation measured in livers lacking Mrp2 was lower that the L 1 slope of normal livers. This result points out that high signal enhancements are not necessarily associated with high hepatocyte uptake. During the rinse period, Bopta remained trapped inside hepatocytes. Such results were published previously in vivo when gadoxetic acid was injected in rodents lacking Mrp2 [26].
Besides Bopta and Meb compartmental distribution, the model identifies several pharmacokinetic parameters obtained by analysing the accumulation of liver or hepatocyte concentrations. During accumulation, the time when agent excretion (in bile canaliculi or back to sinusoids) impacts hepatocytes and liver concentrations (T 0 ) is important. T 0 is lower than 10 min and close for Bopta and Meb in normal livers. Before T 0 , L 1 slope characterises Bopta and Meb entry (in μM/min) into hepatocytes or livers. The value is much higher for Meb than Bopta. After T 0 , the accumulation rates decrease and L 2 slopes are much lower than L 1 slopes for both agents. Concomitant entry and efflux from hepatocytes or livers explain the lower L 2 slopes. Similar biphasic accumulations were previously published following bolus injection of imaging agents in patients [4,[27][28][29]. In these studies, slopes and T 0 were not measured by nonlinear regressions. In our study, we used two linear regressions provided by the software GraphPad Prism [21,22]. Saito et al. [30] also showed a biphasic liver accumulation in patients with or without cirrhosis following a bolus injection of gadoxetic acid. Interestingly, the accumulation rates in the second phase (similar to our L 2 slope) decreased with the severity of cirrhosis.
In clinical practice, the hepatobiliary phase is obtained 20 min (gadoxetic acid) or later (Bopta) after injection. These time-points are superior to T 0 and are situated in the second accumulation phase when liver concentrations depend on both uptake and efflux transporters. Consequently, the clinical time-points underestimate the entry of agents into hepatocytes. Another evidence of early agent excretion from hepatocytes is provided by bile concentrations. For both agents, bile concentrations were higher than 2,000 μM 5 min after the perfusion start. In clinical practice, it is not possible to acquire images every 20 s as done in our study. With simulations, we show that the values of T 0 and L 1 slope are similar until a 5-min acquisition frequency. Another important information for human imaging is that despite discrepancies, liver and hepatocyte parameters of pharmacokinetics were close. The main pharmacokinetic parameter obtained by analysing the decay of Bopta and Meb concentrations was the elimination clearance from hepatocytes. Meb CL el,HC was higher than Bopta CL el,HC and null in cholestatic livers. However, this parameter does not differentiate bile efflux from efflux back into sinusoids. The distinction is unimportant for Meb which is not transported by Mrp3 back into sinusoids. In contrast, Bopta can efflux back to sinusoids [15,19].
The isolated and perfused rat liver is an ex vivo model that allows the mechanistic distribution of agents and tracers in liver compartments. By placing a gamma counter over livers, we can mimic imaging systems such as magnetic resonance imaging (MRI) and single-photon computed emission tomography (SPECT). We can calculate concentrations in all liver compartments. The model clearly distinguishes in situ concentrations from concentrations detected by the counter, knowing that hepatocyte membrane transporters govern in situ concentrations. Liver concentrations detected by the counter is the sum of three in situ concentrations corrected by their respective volume ratio to liver [11]. An important restriction is that a unique volume of interest is investigated that must be delineated in homogenous tissues. The model can be applied to livers with cirrhosis and steatosis [31,32].
The isolated and perfused rat liver is a convenient model because the experimental conditions are well controlled and simplified. It was useful to determine Bopta and Meb compartmental distribution, an issue inaccessible in in vivo imaging. The model is frequently used to investigate the pharmacokinetics of drugs, liver concentrations being measured by collecting biopsies over time. However, this procedure deteriorates the preparation. Such deterioration is avoided by placing a gamma counter over livers. Other experimental models, such as cultured cells or 3D tissues are not appropriate because they do not preserve the liver architecture and liver perfusion flow.
In our model, livers are perfused only through the portal vein, a condition that changes the physiological dualinput liver perfusion. However, hepatic arterial flow represents only 25% of liver blood flow. Moreover, the low portal vein pressure (10-12 mmHg) remained steady during the entire protocol. There is no recirculation of solutions which are discarded after the first pass through sinusoids. This approach is useful to measure the pharmacokinetic parameters we need such as the liver extraction ratio (C in − C out )/C in . Bopta and Meb are not metabolised and the count rates we measure only include parent compounds. We perfuse steady concentrations of agents during 30 min, whilst Meb and Bopta are injected in clinical protocols. Following Bopta injection, human plasma concentrations remain high because the liver extraction ratio is low and Bopta remains in the systemic circulation. In contrast, Meb is rapidly cleared from the systemic circulation in patients and the perfusion we used does not mimic the clinical situation.
In conclusion, our model describes how liver extraction ratios and cholestasis interfere with the compartmental distribution of hepatobiliary agents and reveals new parameters that characterise the accumulation and decay of Bopta and Meb liver concentrations.