P-glycoprotein at the blood-brain barrier: kinetic modeling of ¹¹C-desmethylloperamide in mice using a ¹⁸F-FDG μPET scan to determine the input function

Multidrug transporters, with P-glycoprotein (P-gp) as most investigated, are a large family of ATP-binding cassette membrane proteins, which appear to have been developed as a mechanism to protect the body from harmful substances [1]. In the blood-brain barrier (BBB), P-gp are responsible for pumping toxic compounds out of the brain, resulting in low concentrations of endogenous and exogenous compounds in the brain. Moreover P-gp overexpression has been observed in brain tissues, obtained after surgery in some epileptic patients [2–4], and could also play a role in other neurological diseases. Since these studies are invasive, it would be useful to have a noninvasive method to predict if P-gp is upregulated in patients.

P-gp function can be studied in vivo with radiolabelled substrates. Desmethylloperamide is a metabolite of loperamide, a licensed antidiarrheal agent without central nervous system side effects because P-gp excludes it from the brain [5]. ¹¹C-desmethylloperamide (¹¹C-dLop) is believed to be the most promising tracer to evaluate P-gp function in the brain [6]. One of the standard methods to investigate the P-gp function in particular, is the use of P-gp knock-out mice. The combination with P-gp blocking studies will give an unquestionable indication of the P-gp function [7].

The objective of this study is the implementation of a kinetic model for ¹¹C-dLop and the determination of a typical parameter for P-gp functionality in mice. To set up a kinetic model, it is essential to obtain an arterial input curve, especially if there is no reference region available. Since arterial blood sampling, the gold standard to obtain arterial input curves is very difficult in mice because of the small size and fragility of the mouse blood arteries; an alternative method to acquire the arterial plasma input curve for the kinetic model is proposed.

Biochemical process steps of a tracer in a tissue can be described by an appropriate tracer kinetic model. The behavior of a tracer is usually simplified and described by some mathematical kinetic compartments [11]. This model should be able to estimate the amount of radioactivity in each compartment, and the rate of exchange between these compartments. In PET imaging, these rate constants directly provide information on physiological parameters characterizing the behavior of the tracer in the tissue of interest. In case there is no reference region available, an arterial input curve is necessary to set up a kinetic model. Manual or automatic blood sampling is generally accepted as the gold standard to determine the arterial input curve. Nevertheless, in mice arterial sampling is technically difficult because of the relatively small diameters and fragility of the mouse blood arteries [12]. In addition, the total blood volume of a mouse is very limited (1.7 ml), making repeated blood sampling impossible without affecting the homeostasis of the mice [13]. Alternative methods to obtain an arterial input function are the use of a population database, based on a high number of mice or an arterial input function derived from PET images [14]. Attempts to determine the arterial input function in small animals from PET images were not convincing. Difficult delineation of the left heart ventricle on the PET scan in mice [15] or background signals from surrounding tissues in rats [16] were the main problems. Due to blurred ¹¹C-dLop images on early as well as late time frames, it was impossible to delineate the left heart ventricle accurately. We therefore propose a new image-derived method, using a ¹⁸F-FDG scan after a ¹¹C-dLop scan. Unlike ¹¹C-dLop, ¹⁸F-FDG shows a selective uptake in the myocardium [17–19], making the determination of the left ventricle easy without the problem of spill-in of activity from the surrounding lungs. A comparison between the left heart ventricle time-activity curves (alternative method) and blood counter time-activity curves (corrected for dispersion) showed acceptable graphical agreement. A small AUC difference (3.5%) was observed compared to Green et al. (18%) [20], who did not use a ¹⁸F-FDG scan to delineate the left heart ventricle, but instead a small ROI based on the highest activity in the aorta area on the earliest time frames. Also, the comparison of the K ₁/k ₂ ratio showed analog correlations (6.5%) between standard blood sampling and our proposed method. However, one must realize that the usefulness of our method must be validated for each radioligand because determination of the arterial input function based on the left ventricle could lead to a poor resemblance with the blood sampling input curve especially for radioligands with high myocardial uptake.

Both in wild-type and in P-gp knock-out mice, the percent of parent compound was investigated, resulting in variations probably due to the influence of cyclosporine or to an adaptation of the body to the absence of P-gp efflux transporters. These differences are not an obstacle concerning our experiment because the latter correction was introduced to take these differences into consideration.

Variations in ¹¹C-dLop brain uptake between wild-type and knock-out/cyclosporine-pretreated mice were clearly observed in μPET images and SUVs. Moreover, differences in ¹¹C-dLop uptake in the intestines were observed and could be explained by the absence of P-gp in KO mice resulting in a lower tracer uptake, while in WT mice P-gp located in the intestines pumps the tracer out of the blood into the intestines, resulting in higher uptake. The higher radioactivity in the abdomen of WT mice, as observed in Figure 5, could also be explained as higher uptake in the liver, which is in accordance with results obtained in humans [21]. Nevertheless, kinetic parameters obtained from a compartment model will provide useful mathematical information about the behavior of the tracer. Since no statistical difference in model fittings between the one- and two-compartment model was observed, the simplest model, meaning the one-tissue compartment model, was preferred. This is in accordance to the results mentioned by Kreisl et al. [22]. In a one-tissue compartment model, the tracer behaves in a straightforward manner explained by an uptake in the brain with a speed, represented by the kinetic parameter K ₁, and efflux out of the brain described by k ₂. Binding with any receptors in the brain or metabolisation of the tracer in the brain will not occur in this model. Lazarova et al. [6] already mentioned that ¹¹C-dLop showed no clinical relevant interaction with the opiate receptors in the brain.

The kinetic parameters K ₁ and k ₂ obtained from a one-tissue compartment model of ¹¹C-dLop were evaluated in WT, KO, and WT mice pretreated with cyclosporine. One should expect that K ₁, which represents the passive influx of the tracer in the brain, should not change between the different groups. k ₂, which represents the efflux out of the brain by P-gp transport, was supposed to be lower in KO mice and in the WT mice pretreated with cyclosporine. Our data showed that the K ₁ was statistically lower in WT mice compared to KO or cyclosporine-pretreated WT mice, while the k ₂ was very similar in all tested mice. Kreisl et al. [22] reported the same result after blockage of the P-gp with tariquidar and suggested that tariquidar increased brain uptake of ¹¹C-dLop by increasing its entry (K ₁) rather than by decreasing its efflux (k ₂). The substrate is captured in the endothelial cells, before it enters the intracellular compartment. Therefore, if P-gp captures all of the substrate while in transit through the membrane, its effect is entirely on K ₁. If some of the substrate escapes and has time to interact with the intracellular milieu, and if there is an efflux from the cell, P-gp will both decrease K ₁ and increase k ₂ [23]. Nevertheless, we think that also a time influence of the P-gp transport should be taken into consideration. The course of the brain SUV curve (Figure 6A) in WT mice demonstrates a fast uptake in the brain, followed by a rapid wash out of the brain, resulting in an SUV of 0.25 already 1 min after the tracer injection, while in KO and pretreated WT mice also a fast uptake was observed, followed by an accumulation in the brain of the tracer combined with a slow efflux. The observed different course of the brain curve between WT and KO mice, even as between cyclosporine pretreated WT mice suggests that the duration of the scan could play an important role on the determination of the kinetic parameters in the kinetic model.

This hypothesis was substantiated by the results of K ₁ and k ₂ obtained in a one-tissue compartment model with incorporation of only the first 2 min of dynamic scanning. These results showed a statistically higher k ₂ in WT mice (8.0 ± 0.1) compared to KO (2.3 ± 0.9; P = 0.070) and compared to cyclosporine pretreated WT mice (1.5 ± 0.5; P = 0.002), while K ₁ was statistically not different between the different groups (P > 0.05). This means that during the first 2 min after administration of ¹¹C-dLop, efflux out of the brain is dominated by efflux transporters, while at later time points passive diffusion is more important. The K ₁/k ₂ ratio of WT obtained with the 2-min scan data were statistically different compared to the ratios in KO and compared to cyclosporine-pretreated WT mice. So, we propose K ₁ as a pseudo value, representing a combination of passive influx of ¹¹C-dLop through the BBB and a rapid energy dependent output by P-gp, while k ₂ corresponds to slow passive efflux out of the brain (Figure 8).

The use of an easy to implement ¹¹C-desmethylloperamide kinetic model in mice for imaging P-gp function is presented without arterial blood sampling. The method to determine the input function is based on the delineation of an ROI on the ¹⁸F-FDG scan images and using this ROI on images obtained from a dynamic scan with ¹¹C-dLop. The K ₁ or K ₁/k ₂ ratio obtained from the ¹¹C-dLop tracer kinetic model is a good parameter for the active P-gp rate and can be applied in future experiments to evaluate the role of the upregulation of P-gp in psychotropic drug resistance, such as refractory epilepsy and in tumor resistance to therapy.